List questions from diophantine-equations

Published on 16 Apr 2026 - 0:38

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given N and M count the number of solutions to some diophantine equations, prove that $N>M.$

Published on 14 Apr 2026 - 14:55

258

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Prove that $2\cdot 3^x +1= p^y$ has no solution

Published on 15 Apr 2026 - 23:25

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find all triples $(x,y,z)$ of positive integers such that $x\leq y\leq z$ and $x^3 (y^3 + z^3)=2012(xyz+2)$

Published on 17 Apr 2026 - 0:39

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Solving Cubic Systems of Diophantine Equations

Published on 13 Apr 2026 - 2:58

96

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Solving the Diophantine equation $k^2 = a^2 - 4b + 8$ for $k,a,b$

Published on 16 Apr 2026 - 7:20

88

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Solvability criteria for a a monic almost palindromic quartic diophantine equation

Published on 03 May 2026 - 8:15

65

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What is the purpose of the Markov equation?

Published on 10 Apr 2026 - 21:01

181

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Prove that the equation $u^a - u^b = n!$ has finitely many solutions $(a,b,n)$ in positive integers.

Published on 16 Apr 2026 - 6:17

77

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"Natural" Triangles

Published on 09 Apr 2026 - 17:17

59

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Proving $9a^2+9b^2+9c^2 = (p_1a + q_1b + r_1c)^2 + (p_2a + q_2b + r_2c)^2 + (p_3a + q_3b + r_3c)^2$ where $p_j, q_j, r_j$ are all nonzero integers

Published on 17 Apr 2026 - 12:20

191

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Find all nonnegative integer solutions to $2^a 3^b 5^c - 7^d 9^e 11^f = 4$

Published on 16 Apr 2026 - 11:50

172

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Can 2021 be hypotenuse of a pythagorean triangle?

Published on 08 Apr 2026 - 22:32

199

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Solving a degree-6 Diophantine inequality

Published on 12 Apr 2026 - 23:17

524

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Find the smallest positive integer that can be written as the sum of three cubes of positive integers in two different ways

Published on 11 Apr 2026 - 10:49

List Question

Integral solutions to $A^2=(u^2+uv+2)/2$, $B^2=(v^2+uv+2)/2$, $C^2=1+uv$

given N and M count the number of solutions to some diophantine equations, prove that $N>M.$

Prove that $2\cdot 3^x +1= p^y$ has no solution

find all triples $(x,y,z)$ of positive integers such that $x\leq y\leq z$ and $x^3 (y^3 + z^3)=2012(xyz+2)$

Solving Cubic Systems of Diophantine Equations

Solving the Diophantine equation $k^2 = a^2 - 4b + 8$ for $k,a,b$

Solvability criteria for a a monic almost palindromic quartic diophantine equation

What is the purpose of the Markov equation?

Prove that the equation $u^a - u^b = n!$ has finitely many solutions $(a,b,n)$ in positive integers.

"Natural" Triangles

Proving $9a^2+9b^2+9c^2 = (p_1a + q_1b + r_1c)^2 + (p_2a + q_2b + r_2c)^2 + (p_3a + q_3b + r_3c)^2$ where $p_j, q_j, r_j$ are all nonzero integers

Find all nonnegative integer solutions to $2^a 3^b 5^c - 7^d 9^e 11^f = 4$

Can 2021 be hypotenuse of a pythagorean triangle?

Solving a degree-6 Diophantine inequality

Find the smallest positive integer that can be written as the sum of three cubes of positive integers in two different ways

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