List questions from exponential-diophantine-equations

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$n$ is a square and a cube $a^2 = n = b^3\Rightarrow n\equiv 0,1\pmod{7}$

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Solve $3^a-5^b=2$ for integers a and b.

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Solve Diophantine equation: $2^x=5^y+3$ for non-negative integers $x,y$.

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Find all positive integers satisfying $a^{b^2}=b^a$.

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Find integers $x > 1, y > 1$ such that $(y^x+1) \mid (x^y+1)$

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Does there exist $n\in\mathbb{N}$ such that $5^n-2^n$ is a perfect square?

Published on 23 Feb 2026 - 2:09

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Find all $n\in\mathbb N$ such that $10^n-6^n$ is a perfect square

Published on 23 Feb 2026 - 2:12

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Find the zeros of $4^x+6^{x^2}=5^x+5^{x^2}$

Published on 23 Feb 2026 - 2:13

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diophantine equation $(1+\ldots+n)^k=1^l+\ldots+n^l$

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What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$

Published on 23 Feb 2026 - 2:09

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An exponential Diophantine equation.

Published on 23 Feb 2026 - 2:07

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How to find the general integer solution to an equation involving modulo with an unknown exponent?

Published on 23 Feb 2026 - 2:16

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Does every positive power of $7$ contain $2$ in their ternary representation?

Published on 23 Feb 2026 - 2:12

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No positive integer solutions $(x, y, z)$ to the diophantine equation $2x^6+3y^6=z^3$

Published on 23 Feb 2026 - 2:13

List Question

The diophantine equation $5\times 2^{x-4}=3^y-1$

$n$ is a square and a cube $a^2 = n = b^3\Rightarrow n\equiv 0,1\pmod{7}$

Solve $3^a-5^b=2$ for integers a and b.

Solve Diophantine equation: $2^x=5^y+3$ for non-negative integers $x,y$.

Find all positive integers satisfying $a^{b^2}=b^a$.

Find integers $x > 1, y > 1$ such that $(y^x+1) \mid (x^y+1)$

Does there exist $n\in\mathbb{N}$ such that $5^n-2^n$ is a perfect square?

Find all $n\in\mathbb N$ such that $10^n-6^n$ is a perfect square

Find the zeros of $4^x+6^{x^2}=5^x+5^{x^2}$

diophantine equation $(1+\ldots+n)^k=1^l+\ldots+n^l$

What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$

An exponential Diophantine equation.

How to find the general integer solution to an equation involving modulo with an unknown exponent?

Does every positive power of $7$ contain $2$ in their ternary representation?

No positive integer solutions $(x, y, z)$ to the diophantine equation $2x^6+3y^6=z^3$

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