List questions from diophantine-equations

Published on 19 Feb 2016 - 21:49

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Diophantine equation in the integers

Published on 20 Feb 2016 - 7:22

567

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Show that there exist no $a, b, c \in \mathbb Z^+$ such that $a^3 + 2b^3 = 4c^3$

Published on 20 Feb 2016 - 10:05

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proof - if $x^2 + y^2 + z^2 = 2xyz$ then $x = y = z = 0$

Published on 20 Feb 2016 - 11:56

91

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$x^3 + 5x + 6 = 3\cdot 2^{1+x-k} $

Published on 20 Feb 2016 - 15:43

352

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Trying to solve the equation $\sum_{i=0}^{t}(-1)^i\binom{m}{i}\binom{n-m}{t-i}=0 $ for non-negative integers $m,n,t$

Published on 20 Feb 2016 - 17:28

154

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Multiple solutions to Diophantine Equation $X = \tfrac{1}{2} xy(x^2 - y^2) $

Published on 28 Mar 2026 - 4:42

85

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how to solve $x^2-y^2=(2n-1)^2$

Published on 23 Feb 2016 - 16:15

136

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Solving diophantine equations

Published on 01 Apr 2026 - 17:08

1k

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Primes of the form $x^3+y^3+z^3 - 3xyz$

Published on 24 Feb 2016 - 22:47

3.3k

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How to solve these two simultaneous "divisibilities" : $n+1\mid m^2+1$ and $m+1\mid n^2+1$

Published on 31 Mar 2026 - 10:10

509

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Diophantine Equation: how to find k such as solutions are natural numbers?

Published on 25 Mar 2026 - 22:06

213

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Special Euler bricks and $x^2(y^2-1)^2+y^2(x^2-1)^2=z^2$

Published on 28 Mar 2026 - 6:09

108

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Solving $2(n-1)n(n+1)(n+2)=(m-3)(m+3)$

Published on 08 Apr 2026 - 0:44

1.8k

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When is $991n^2 +1$ a perfect square?

Published on 31 Mar 2026 - 10:06

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Looking for a general method for this type/class of Diophantine equation

Diophantine equation in the integers

Show that there exist no $a, b, c \in \mathbb Z^+$ such that $a^3 + 2b^3 = 4c^3$

proof - if $x^2 + y^2 + z^2 = 2xyz$ then $x = y = z = 0$

$x^3 + 5x + 6 = 3\cdot 2^{1+x-k} $

Trying to solve the equation $\sum_{i=0}^{t}(-1)^i\binom{m}{i}\binom{n-m}{t-i}=0 $ for non-negative integers $m,n,t$

Multiple solutions to Diophantine Equation $X = \tfrac{1}{2} xy(x^2 - y^2) $

how to solve $x^2-y^2=(2n-1)^2$

Solving diophantine equations

Primes of the form $x^3+y^3+z^3 - 3xyz$

How to solve these two simultaneous "divisibilities" : $n+1\mid m^2+1$ and $m+1\mid n^2+1$

Diophantine Equation: how to find k such as solutions are natural numbers?

Special Euler bricks and $x^2(y^2-1)^2+y^2(x^2-1)^2=z^2$

Solving $2(n-1)n(n+1)(n+2)=(m-3)(m+3)$

When is $991n^2 +1$ a perfect square?

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