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 $kgeq 3$
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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 $kgeq 3$
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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
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$begingroup$
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
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add a comment |
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$begingroup$
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 |
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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