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$\frac{1}{a} = \frac{1}{b} + \frac{1}{c} - \frac{1}{abc}$ and $a^2 + b^2 = c^2$

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#contest-math #systems-of-equations #diophantine-equations #pythagorean-triples
56
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Are there coprime nonzero integers $u,v,w$ such that $2u(u^2+pv^2)=w^p$ where $p>3$?

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#diophantine-equations
1.5k
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Uses of Vieta Jumping in research mathematics?

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#number-theory #diophantine-equations #math-history #vieta-jumping
78
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Find all integer solutions to $n^2 - n = c\cdot 2^{J+1}$

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#number-theory #elementary-number-theory #discrete-mathematics #diophantine-equations
49
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Can you prove mu-recursive functions are Diophantine without bounded universal quantifiers?

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#logic #diophantine-equations #computability #exponential-diophantine-equations
67
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Reference request: there are only two integer solutions to $2^{2a} + 3^{2b} = 5^c$.

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#number-theory #reference-request #diophantine-equations #pythagorean-triples
164
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Positive integer solutions to $y^2=a(1+xy-x^2)$

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#real-analysis #sequences-and-series #elementary-number-theory #algebraic-geometry #diophantine-equations
116
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Positive integer solutions to $pxy+x+y=p\#$

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#number-theory #prime-numbers #diophantine-equations #prime-factorization
81
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Ramanujan-Nagell-ish diophantine equation

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#number-theory #modular-arithmetic #divisibility #diophantine-equations
80
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Solution of the Diophantine equation

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#number-theory #diophantine-equations #exponential-diophantine-equations
89
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Are these the only "intersections" between the following series, and why all of them are multiples of $10$

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#sequences-and-series #algebra-precalculus #diophantine-equations #recreational-mathematics
115
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How to solve this diophantine equation: $x^2+2y^2=x^2y^2-2000$

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#algebra-precalculus #contest-math #diophantine-equations
82
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Find the integer solutions for an equation with rational fraction whose degree depends on another integer variable

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#elementary-number-theory #contest-math #diophantine-equations
81
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How to solve Linear diophantine equation ax+by=4ab

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#linear-algebra #diophantine-equations #linear-diophantine-equations
139
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Diophantine with factorials

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#number-theory #diophantine-equations #factorial #integers

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