Diophantine Equations of Degree 2 Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Strange Cubic Diophantine EquationsSecond degree Diophantine equationsDiophantine equation without unique formula for solutionsDiophantine Equations involving cubesHow to solve simultaneous modulus / diophantine equationsClassifying Diophantine EquationsFinding other solutions to diophantine equationsHyperbolic Diophantine Equations: Application of Euclidean Algorithm?Solution to rational Diophantine equations in fixed pointInteger solutions to a Diophantine Equation
How to make an animal which can only breed for a certain number of generations?
Can gravitational waves pass through a black hole?
Understanding piped commands in GNU/Linux
Centre cell vertically in tabularx
A question about the degree of an extension field
Why is there so little support for joining EFTA in the British parliament?
As a dual citizen, my US passport will expire one day after traveling to the US. Will this work?
In musical terms, what properties are varied by the human voice to produce different words / syllables?
Why are two-digit numbers in Jonathan Swift's "Gulliver's Travels" (1726) written in "German style"?
What is "Lambda" in Heston's original paper on stochastic volatility models?
Do i imagine the linear (straight line) homotopy in a correct way?
Twin's vs. Twins'
The Nth Gryphon Number
Did pre-Columbian Americans know the spherical shape of the Earth?
How can I prevent/balance waiting and turtling as a response to cooldown mechanics
French equivalents of おしゃれは足元から (Every good outfit starts with the shoes)
What did Turing mean when saying that "machines cannot give rise to surprises" is due to a fallacy?
Short story about astronauts fertilizing soil with their own bodies
Pointing to problems without suggesting solutions
Fit odd number of triplets in a measure?
Does the transliteration of 'Dravidian' exist in Hindu scripture? Does 'Dravida' refer to a Geographical area or an ethnic group?
Is it OK to use the testing sample to compare algorithms?
Marquee sign letters
First paper to introduce the "principal-agent problem"
Diophantine Equations of Degree 2
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Strange Cubic Diophantine EquationsSecond degree Diophantine equationsDiophantine equation without unique formula for solutionsDiophantine Equations involving cubesHow to solve simultaneous modulus / diophantine equationsClassifying Diophantine EquationsFinding other solutions to diophantine equationsHyperbolic Diophantine Equations: Application of Euclidean Algorithm?Solution to rational Diophantine equations in fixed pointInteger solutions to a Diophantine Equation
$begingroup$
During my studies, I have seen equations of this form $$xy+bx+cy+d=0$$ Is there a way to find solutions of equations of this form or the number of solutions of equations of this form without factoring or checking within a range?
diophantine-equations
asked Apr 2 at 15:06
Quote DaveQuote Dave
336
$endgroup$
add a comment |
$begingroup$
During my studies, I have seen equations of this form $$xy+bx+cy+d=0$$ Is there a way to find solutions of equations of this form or the number of solutions of equations of this form without factoring or checking within a range?
diophantine-equations
asked Apr 2 at 15:06
Quote DaveQuote Dave
336
$endgroup$
$begingroup$
That's the same as $(x+c)(y+b)=bc-d$, so really it is just a factoring problem.
$endgroup$
– Lord Shark the Unknown
Apr 2 at 15:56
add a comment |
$begingroup$
During my studies, I have seen equations of this form $$xy+bx+cy+d=0$$ Is there a way to find solutions of equations of this form or the number of solutions of equations of this form without factoring or checking within a range?
diophantine-equations
asked Apr 2 at 15:06
Quote DaveQuote Dave
336
$endgroup$
During my studies, I have seen equations of this form $$xy+bx+cy+d=0$$ Is there a way to find solutions of equations of this form or the number of solutions of equations of this form without factoring or checking within a range?
diophantine-equations
diophantine-equations
asked Apr 2 at 15:06
Quote DaveQuote Dave
336
asked Apr 2 at 15:06
Quote DaveQuote Dave
336
asked Apr 2 at 15:06
Quote DaveQuote Dave
336
asked Apr 2 at 15:06
Quote DaveQuote Dave
336
asked Apr 2 at 15:06
Quote DaveQuote Dave
336
336
$begingroup$
That's the same as $(x+c)(y+b)=bc-d$, so really it is just a factoring problem.
$endgroup$
– Lord Shark the Unknown
Apr 2 at 15:56
add a comment |
$begingroup$
That's the same as $(x+c)(y+b)=bc-d$, so really it is just a factoring problem.
$endgroup$
– Lord Shark the Unknown
Apr 2 at 15:56
$begingroup$
That's the same as $(x+c)(y+b)=bc-d$, so really it is just a factoring problem.
$endgroup$
– Lord Shark the Unknown
Apr 2 at 15:56
$begingroup$
That's the same as $(x+c)(y+b)=bc-d$, so really it is just a factoring problem.
$endgroup$
– Lord Shark the Unknown
Apr 2 at 15:56
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint
Assuming $b,c,d$ are given integers,
$$(b+y)(c+x)=bc-d$$
Or
$$y=-dfracbx+dc+x=-b+?$$
answered Apr 2 at 15:08
lab bhattacharjeelab bhattacharjee
229k15159279
$endgroup$
$begingroup$
I don't understand what you mean by this. Could you clarify?
$endgroup$
– Quote Dave
Apr 2 at 21:03
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%2f3171972%2fdiophantine-equations-of-degree-2%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
$begingroup$
Hint
Assuming $b,c,d$ are given integers,
$$(b+y)(c+x)=bc-d$$
Or
$$y=-dfracbx+dc+x=-b+?$$
answered Apr 2 at 15:08
lab bhattacharjeelab bhattacharjee
229k15159279
$endgroup$
$begingroup$
I don't understand what you mean by this. Could you clarify?
$endgroup$
– Quote Dave
Apr 2 at 21:03
add a comment |
$begingroup$
Hint
Assuming $b,c,d$ are given integers,
$$(b+y)(c+x)=bc-d$$
Or
$$y=-dfracbx+dc+x=-b+?$$
answered Apr 2 at 15:08
lab bhattacharjeelab bhattacharjee
229k15159279
$endgroup$
$begingroup$
I don't understand what you mean by this. Could you clarify?
$endgroup$
– Quote Dave
Apr 2 at 21:03
add a comment |
$begingroup$
Hint
Assuming $b,c,d$ are given integers,
$$(b+y)(c+x)=bc-d$$
Or
$$y=-dfracbx+dc+x=-b+?$$
answered Apr 2 at 15:08
lab bhattacharjeelab bhattacharjee
229k15159279
$endgroup$
Hint
Assuming $b,c,d$ are given integers,
$$(b+y)(c+x)=bc-d$$
Or
$$y=-dfracbx+dc+x=-b+?$$
answered Apr 2 at 15:08
lab bhattacharjeelab bhattacharjee
229k15159279
answered Apr 2 at 15:08
lab bhattacharjeelab bhattacharjee
229k15159279
answered Apr 2 at 15:08
lab bhattacharjeelab bhattacharjee
229k15159279
answered Apr 2 at 15:08
lab bhattacharjeelab bhattacharjee
229k15159279
229k15159279
$begingroup$
I don't understand what you mean by this. Could you clarify?
$endgroup$
– Quote Dave
Apr 2 at 21:03
add a comment |
$begingroup$
I don't understand what you mean by this. Could you clarify?
$endgroup$
– Quote Dave
Apr 2 at 21:03
$begingroup$
I don't understand what you mean by this. Could you clarify?
$endgroup$
– Quote Dave
Apr 2 at 21:03
$begingroup$
I don't understand what you mean by this. Could you clarify?
$endgroup$
– Quote Dave
Apr 2 at 21:03
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%2f3171972%2fdiophantine-equations-of-degree-2%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
$begingroup$
That's the same as $(x+c)(y+b)=bc-d$, so really it is just a factoring problem.
$endgroup$
– Lord Shark the Unknown
Apr 2 at 15:56