List questions from vieta-jumping

Published on 30 Aug 2015 - 23:01

809

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Diophantine equation $(x+y)(x+y+1) - kxy = 0$

Published on 01 Sep 2015 - 18:36

138

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Find the postive integers such $xy+x+y\mid x^2+y^2-2$

Published on 03 Oct 2015 - 14:05

352

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Vieta Jumping and Hurwitz 1907

Published on 07 Oct 2015 - 21:52

531

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Find the integer values of c

Published on 18 Mar 2026 - 23:48

532

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For which integers $a,b$ does $ab-1$ divide $a^3+1$?

Published on 27 Feb 2026 - 20:10

322

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How to prove that $a_{n}$ must be of the form $a^2+b^2$?

Published on 01 Jun 2013 - 4:03

214

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General question about 'vieta jumping'

Published on 28 Aug 2013 - 2:35

22.2k

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IMO 1988, problem 6

Published on 24 Mar 2026 - 12:40

1.5k

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Diophantine quartic equation in four variables

Published on 09 Jan 2014 - 2:42

194

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Diophantine quartic equation in four variables, part deux

Published on 11 Jan 2014 - 4:20

366

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Finding all primes $p,q$ with $p^2+q^2=9pq-13$

Published on 13 Jun 2017 - 3:45

868

Views

Let $x$, $y$ and $z$ be natural numbers satisfying $x^2 + y^2 + 1 = xyz$. Prove that $z = 3$.

Published on 22 Jul 2017 - 21:08

179

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A conjecture inspired by a famous contest problem

Published on 01 Aug 2017 - 20:03

266

Views

How prove infinitely many postive integers triples $(x,y,z)$ such $(x+y+z)^2+2(x+y+z)=5(xy+yz+zx)$

Published on 20 Aug 2017 - 4:35

List Question

Proving that all terms in sequence are positive integers (Recursive)

Diophantine equation $(x+y)(x+y+1) - kxy = 0$

Find the postive integers such $xy+x+y\mid x^2+y^2-2$

Vieta Jumping and Hurwitz 1907

Find the integer values of c

For which integers $a,b$ does $ab-1$ divide $a^3+1$?

How to prove that $a_{n}$ must be of the form $a^2+b^2$?

General question about 'vieta jumping'

IMO 1988, problem 6

Diophantine quartic equation in four variables

Diophantine quartic equation in four variables, part deux

Finding all primes $p,q$ with $p^2+q^2=9pq-13$

Let $x$, $y$ and $z$ be natural numbers satisfying $x^2 + y^2 + 1 = xyz$. Prove that $z = 3$.

A conjecture inspired by a famous contest problem

How prove infinitely many postive integers triples $(x,y,z)$ such $(x+y+z)^2+2(x+y+z)=5(xy+yz+zx)$

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