Is the problem Find all $x,y in mathbfN$ such that $binomx2 = binomy5$ solved? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Solving quadratic Diophantine equations: $5n^2+2n+1=y^2$How to solve Linear Diophantine equations?How to think about minors of the rectangular matrix in the context of a system of Diophantine linear equationsNonlinear system Diophantus.How to solve these system of linear equations?How can this problem be solved using continued fractions?A Diophantine equation involving factorialSolution of Certain Number Theoretic Problems.On diophantine equations involving Stirling numbers of the second kind I: the equation $mbrace k-nbrace k=z^k$ for fixed integers $kgeq 3$
1-probability to calculate two events in a row
How can I prevent/balance waiting and turtling as a response to cooldown mechanics
Strange behavior of Object.defineProperty() in JavaScript
What's the point of the test set?
How many time has Arya actually used Needle?
Putting class ranking in CV, but against dept guidelines
The Nth Gryphon Number
An adverb for when you're not exaggerating
One-one communication
Does the Mueller report show a conspiracy between Russia and the Trump Campaign?
Lagrange four-squares theorem --- deterministic complexity
How does light 'choose' between wave and particle behaviour?
What to do with repeated rejections for phd position
What is the chair depicted in Cesare Maccari's 1889 painting "Cicerone denuncia Catilina"?
What is the meaning of 'breadth' in breadth first search?
Project Euler #1 in C++
How to run automated tests after each commit?
Why are my pictures showing a dark band on one edge?
Co-worker has annoying ringtone
Why weren't discrete x86 CPUs ever used in game hardware?
Converted a Scalar function to a TVF function for parallel execution-Still running in Serial mode
Is there hard evidence that the grant peer review system performs significantly better than random?
Trademark violation for app?
Tannaka duality for semisimple groups
Is the problem Find all $x,y in mathbfN$ such that $binomx2 = binomy5$ solved?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Solving quadratic Diophantine equations: $5n^2+2n+1=y^2$How to solve Linear Diophantine equations?How to think about minors of the rectangular matrix in the context of a system of Diophantine linear equationsNonlinear system Diophantus.How to solve these system of linear equations?How can this problem be solved using continued fractions?A Diophantine equation involving factorialSolution of Certain Number Theoretic Problems.On diophantine equations involving Stirling numbers of the second kind I: the equation $mbrace k-nbrace k=z^k$ for fixed integers $kgeq 3$
$begingroup$
I was recently browsing and came upon this document which gives some open problems involving Diophantine Equations.
Document: http://www.math.leidenuniv.nl/~evertse/07-workshop-problems.pdf
Upon searching a bit, I found that the first problem given has been solved. Is the second problem also solved?
The problem is Find all $x,y in mathbfN$ such that $binomx2 = binomy5$.
number-theory diophantine-equations combinatorial-number-theory
asked Apr 2 at 1:02
blue applesblue apples
454
$endgroup$
add a comment |
$begingroup$
I was recently browsing and came upon this document which gives some open problems involving Diophantine Equations.
Document: http://www.math.leidenuniv.nl/~evertse/07-workshop-problems.pdf
Upon searching a bit, I found that the first problem given has been solved. Is the second problem also solved?
The problem is Find all $x,y in mathbfN$ such that $binomx2 = binomy5$.
number-theory diophantine-equations combinatorial-number-theory
asked Apr 2 at 1:02
blue applesblue apples
454
$endgroup$
1
$begingroup$
It looks a bit misleading. The problem is to find all $x, y in mathbbN$ with $binomx2 = binomy5$. It sounds like you are claiming that they are equal for all $x, y$, which they're not of course.
$endgroup$
– Randall
Apr 2 at 1:04
$begingroup$
google.com/amp/www.algebra.com/algebra/homework/Permutations/…
$endgroup$
– lab bhattacharjee
Apr 2 at 1:30
$begingroup$
@Randall thanks for that - have edited the question accordingly....@lab bhattacharjee I fail to see what that link has to do with my question or am I misunderstanding something?
$endgroup$
– blue apples
Apr 2 at 1:35
2
$begingroup$
de Weger, Equal binomial coefficients: some elementary considerations, J. Number Thy. 63 (1997) 373-386, gives the nontrivial examples 78-choose-2 equals 15-choose-5 equals 3003, and 153-choose-2 equals 19-choose-5 equals 11628, and conjectures there are no others.
$endgroup$
– Gerry Myerson
Apr 2 at 3:14
add a comment |
$begingroup$
I was recently browsing and came upon this document which gives some open problems involving Diophantine Equations.
Document: http://www.math.leidenuniv.nl/~evertse/07-workshop-problems.pdf
Upon searching a bit, I found that the first problem given has been solved. Is the second problem also solved?
The problem is Find all $x,y in mathbfN$ such that $binomx2 = binomy5$.
number-theory diophantine-equations combinatorial-number-theory
asked Apr 2 at 1:02
blue applesblue apples
454
$endgroup$
I was recently browsing and came upon this document which gives some open problems involving Diophantine Equations.
Document: http://www.math.leidenuniv.nl/~evertse/07-workshop-problems.pdf
Upon searching a bit, I found that the first problem given has been solved. Is the second problem also solved?
The problem is Find all $x,y in mathbfN$ such that $binomx2 = binomy5$.
number-theory diophantine-equations combinatorial-number-theory
number-theory diophantine-equations combinatorial-number-theory
asked Apr 2 at 1:02
blue applesblue apples
454
asked Apr 2 at 1:02
blue applesblue apples
454
edited Apr 2 at 1:34
blue apples
asked Apr 2 at 1:02
blue applesblue apples
454
asked Apr 2 at 1:02
blue applesblue apples
454
asked Apr 2 at 1:02
blue applesblue apples
454
454
1
$begingroup$
It looks a bit misleading. The problem is to find all $x, y in mathbbN$ with $binomx2 = binomy5$. It sounds like you are claiming that they are equal for all $x, y$, which they're not of course.
$endgroup$
– Randall
Apr 2 at 1:04
$begingroup$
google.com/amp/www.algebra.com/algebra/homework/Permutations/…
$endgroup$
– lab bhattacharjee
Apr 2 at 1:30
$begingroup$
@Randall thanks for that - have edited the question accordingly....@lab bhattacharjee I fail to see what that link has to do with my question or am I misunderstanding something?
$endgroup$
– blue apples
Apr 2 at 1:35
2
$begingroup$
de Weger, Equal binomial coefficients: some elementary considerations, J. Number Thy. 63 (1997) 373-386, gives the nontrivial examples 78-choose-2 equals 15-choose-5 equals 3003, and 153-choose-2 equals 19-choose-5 equals 11628, and conjectures there are no others.
$endgroup$
– Gerry Myerson
Apr 2 at 3:14
add a comment |
1
$begingroup$
It looks a bit misleading. The problem is to find all $x, y in mathbbN$ with $binomx2 = binomy5$. It sounds like you are claiming that they are equal for all $x, y$, which they're not of course.
$endgroup$
– Randall
Apr 2 at 1:04
$begingroup$
google.com/amp/www.algebra.com/algebra/homework/Permutations/…
$endgroup$
– lab bhattacharjee
Apr 2 at 1:30
$begingroup$
@Randall thanks for that - have edited the question accordingly....@lab bhattacharjee I fail to see what that link has to do with my question or am I misunderstanding something?
$endgroup$
– blue apples
Apr 2 at 1:35
2
$begingroup$
de Weger, Equal binomial coefficients: some elementary considerations, J. Number Thy. 63 (1997) 373-386, gives the nontrivial examples 78-choose-2 equals 15-choose-5 equals 3003, and 153-choose-2 equals 19-choose-5 equals 11628, and conjectures there are no others.
$endgroup$
– Gerry Myerson
Apr 2 at 3:14
1
1
$begingroup$
It looks a bit misleading. The problem is to find all $x, y in mathbbN$ with $binomx2 = binomy5$. It sounds like you are claiming that they are equal for all $x, y$, which they're not of course.
$endgroup$
– Randall
Apr 2 at 1:04
$begingroup$
It looks a bit misleading. The problem is to find all $x, y in mathbbN$ with $binomx2 = binomy5$. It sounds like you are claiming that they are equal for all $x, y$, which they're not of course.
$endgroup$
– Randall
Apr 2 at 1:04
$begingroup$
google.com/amp/www.algebra.com/algebra/homework/Permutations/…
$endgroup$
– lab bhattacharjee
Apr 2 at 1:30
$begingroup$
google.com/amp/www.algebra.com/algebra/homework/Permutations/…
$endgroup$
– lab bhattacharjee
Apr 2 at 1:30
$begingroup$
@Randall thanks for that - have edited the question accordingly....@lab bhattacharjee I fail to see what that link has to do with my question or am I misunderstanding something?
$endgroup$
– blue apples
Apr 2 at 1:35
$begingroup$
@Randall thanks for that - have edited the question accordingly....@lab bhattacharjee I fail to see what that link has to do with my question or am I misunderstanding something?
$endgroup$
– blue apples
Apr 2 at 1:35
2
2
$begingroup$
de Weger, Equal binomial coefficients: some elementary considerations, J. Number Thy. 63 (1997) 373-386, gives the nontrivial examples 78-choose-2 equals 15-choose-5 equals 3003, and 153-choose-2 equals 19-choose-5 equals 11628, and conjectures there are no others.
$endgroup$
– Gerry Myerson
Apr 2 at 3:14
$begingroup$
de Weger, Equal binomial coefficients: some elementary considerations, J. Number Thy. 63 (1997) 373-386, gives the nontrivial examples 78-choose-2 equals 15-choose-5 equals 3003, and 153-choose-2 equals 19-choose-5 equals 11628, and conjectures there are no others.
$endgroup$
– Gerry Myerson
Apr 2 at 3:14
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
According to Blokhuis, Brouwer, and de Weger, Binomial collisions and near collisions, Integers 17 (2017) #A64, the question was settled in Bugeaud, Mignotte, Siksek, Stoll, and Tengely, Integral points on hyperelliptic curves, Algebra Number Theory 2 (2008) 859-885; there are no nontrivial solutions, other than those given in the comment.
answered Apr 2 at 3:27
Gerry MyersonGerry Myerson
148k8152306
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3171337%2fis-the-problem-find-all-x-y-in-mathbfn-such-that-binomx2-binomy%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
According to Blokhuis, Brouwer, and de Weger, Binomial collisions and near collisions, Integers 17 (2017) #A64, the question was settled in Bugeaud, Mignotte, Siksek, Stoll, and Tengely, Integral points on hyperelliptic curves, Algebra Number Theory 2 (2008) 859-885; there are no nontrivial solutions, other than those given in the comment.
answered Apr 2 at 3:27
Gerry MyersonGerry Myerson
148k8152306
$endgroup$
add a comment |
$begingroup$
According to Blokhuis, Brouwer, and de Weger, Binomial collisions and near collisions, Integers 17 (2017) #A64, the question was settled in Bugeaud, Mignotte, Siksek, Stoll, and Tengely, Integral points on hyperelliptic curves, Algebra Number Theory 2 (2008) 859-885; there are no nontrivial solutions, other than those given in the comment.
answered Apr 2 at 3:27
Gerry MyersonGerry Myerson
148k8152306
$endgroup$
add a comment |
$begingroup$
According to Blokhuis, Brouwer, and de Weger, Binomial collisions and near collisions, Integers 17 (2017) #A64, the question was settled in Bugeaud, Mignotte, Siksek, Stoll, and Tengely, Integral points on hyperelliptic curves, Algebra Number Theory 2 (2008) 859-885; there are no nontrivial solutions, other than those given in the comment.
answered Apr 2 at 3:27
Gerry MyersonGerry Myerson
148k8152306
$endgroup$
According to Blokhuis, Brouwer, and de Weger, Binomial collisions and near collisions, Integers 17 (2017) #A64, the question was settled in Bugeaud, Mignotte, Siksek, Stoll, and Tengely, Integral points on hyperelliptic curves, Algebra Number Theory 2 (2008) 859-885; there are no nontrivial solutions, other than those given in the comment.
answered Apr 2 at 3:27
Gerry MyersonGerry Myerson
148k8152306
answered Apr 2 at 3:27
Gerry MyersonGerry Myerson
148k8152306
answered Apr 2 at 3:27
Gerry MyersonGerry Myerson
148k8152306
answered Apr 2 at 3:27
Gerry MyersonGerry Myerson
148k8152306
148k8152306
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3171337%2fis-the-problem-find-all-x-y-in-mathbfn-such-that-binomx2-binomy%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
It looks a bit misleading. The problem is to find all $x, y in mathbbN$ with $binomx2 = binomy5$. It sounds like you are claiming that they are equal for all $x, y$, which they're not of course.
$endgroup$
– Randall
Apr 2 at 1:04
$begingroup$
google.com/amp/www.algebra.com/algebra/homework/Permutations/…
$endgroup$
– lab bhattacharjee
Apr 2 at 1:30
$begingroup$
@Randall thanks for that - have edited the question accordingly....@lab bhattacharjee I fail to see what that link has to do with my question or am I misunderstanding something?
$endgroup$
– blue apples
Apr 2 at 1:35
2
$begingroup$
de Weger, Equal binomial coefficients: some elementary considerations, J. Number Thy. 63 (1997) 373-386, gives the nontrivial examples 78-choose-2 equals 15-choose-5 equals 3003, and 153-choose-2 equals 19-choose-5 equals 11628, and conjectures there are no others.
$endgroup$
– Gerry Myerson
Apr 2 at 3:14