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

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#sequences-and-series #contest-math #recursion #vieta-jumping
812
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Diophantine equation $(x+y)(x+y+1) - kxy = 0$

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#number-theory #elementary-number-theory #diophantine-equations #vieta-jumping
140
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Find the postive integers such $xy+x+y\mid x^2+y^2-2$

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#number-theory #vieta-jumping
355
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Vieta Jumping and Hurwitz 1907

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#number-theory #diophantine-equations #quadratic-forms #vieta-jumping
532
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Find the integer values of c

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#number-theory #diophantine-equations #vieta-jumping
533
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For which integers $a,b$ does $ab-1$ divide $a^3+1$?

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#elementary-number-theory #elliptic-curves #vieta-jumping
323
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How to prove that $a_{n}$ must be of the form $a^2+b^2$?

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#recurrence-relations #vieta-jumping
215
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General question about 'vieta jumping'

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#number-theory #vieta-jumping
22.2k
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IMO 1988, problem 6

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#elementary-number-theory #contest-math #square-numbers #vieta-jumping
1.5k
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Diophantine quartic equation in four variables

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#geometry #diophantine-equations #vieta-jumping
195
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Diophantine quartic equation in four variables, part deux

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#geometry #diophantine-equations #vieta-jumping
367
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Finding all primes $p,q$ with $p^2+q^2=9pq-13$

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#number-theory #elementary-number-theory #diophantine-equations #vieta-jumping
869
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Let $x$, $y$ and $z$ be natural numbers satisfying $x^2 + y^2 + 1 = xyz$. Prove that $z = 3$.

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#elementary-number-theory #diophantine-equations #vieta-jumping
180
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A conjecture inspired by a famous contest problem

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#elementary-number-theory #divisibility #conjectures #vieta-jumping
267
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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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#number-theory #elementary-number-theory #diophantine-equations #vieta-jumping

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