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How to prove that $x^2+1=5^y$ has no positive integer solutions for $y\geq 2$?

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#number-theory #diophantine-equations
1.7k
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Integer points on a hyperbola

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#diophantine-equations #vieta-jumping
237
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Simplest nontrivial example of an L-function yielding information about a Diophantine equation

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#diophantine-equations #l-functions
322
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Solution to Mordell's Equation $y^2=x^3+4$

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#diophantine-equations #mordell-curves
216
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Goldbach's conjecture and Diophantine equations.

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#number-theory #diophantine-equations
249
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simple hyperbolic Diophantine equation

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#diophantine-equations
282
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Help prove $p^4 + 4q^4$ is never a perfect square?

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#number-theory #elementary-number-theory #diophantine-equations #pythagorean-triples
206
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Is it possible to narrow down a domain of possible counter-examples to the Collatz Conjecture?

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#number-theory #diophantine-equations #conjectures #collatz-conjecture
55
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Area of the polygon with coordinates that satisfy the equation

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#diophantine-equations
60
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Solving in Integer sequences

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#systems-of-equations #diophantine-equations
117
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What are the properties of abundancy numbers?

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#elementary-number-theory #diophantine-equations #big-list #divisor-sum
145
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Find all pairs of intergers satisfying $x^2+11 = y^4 -xy$ and $y^2 + xy= 30 $

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#elementary-number-theory #systems-of-equations #diophantine-equations
132
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Solving equations in $\mathbb{Z}/p\mathbb{Z}$ versus $\mathbb{Q}_p$.

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#number-theory #algebraic-geometry #diophantine-equations #p-adic-number-theory #arithmetic-geometry
104
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Algebra - Solving for three unknowns.

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#elementary-number-theory #diophantine-equations
2.6k
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Integer solutions to $x^3=y^3+2y+1$?

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#algebra-precalculus #elementary-number-theory #contest-math #diophantine-equations #cubics

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