List questions from diophantine-equations

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A problem from Observations on Arithmetica

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Solve $2^x+y^2=z!$

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If the equation $x^2 = (2^{2^y} + 1)^s + 2^t$ holds, can $t$ be odd?

Published on 15 Apr 2026 - 19:51

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$\sqrt{2^2} = 2$, $\sqrt{2^4} = 2^2 = 4$, $\sqrt{2^6} = 8 \neq 6$, $\ldots$

Published on 16 Apr 2026 - 15:51

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When does $p^s = 2^t + 1$ have a solution, for $t$ odd and $p$ prime?

Published on 16 Apr 2026 - 10:07

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$\sum_1^I a_i 2^i + \sum_1^J b_j 3^j = \sum_1^I c_i 2^i + \sum_1^J d_j 3^j$

Published on 16 Apr 2026 - 11:49

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Is this an uncomputable function?

Published on 11 Apr 2026 - 11:09

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Reciprocal Solution to the Ramberg Osgood Equation

Published on 11 Apr 2026 - 16:16

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Fundamental solutions of the positive Pell Equation

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Prove that the equation $x^3 + 117y^3 = 5 $ has no integer solution $x, y$

Published on 16 Apr 2026 - 1:26

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On the square values of a certain polynomial

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Find all integers $x$ and $y$ such that $4y^2=x^7+1$

Published on 15 Apr 2026 - 10:58

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Why are the minimal solutions of the Pell equation $x^2-(n^2-3)y^2=1$ larger than average when $3 \not | n$?

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calculate the sum of 5 numbers, knowing the product of their values minus 4

Published on 12 Apr 2026 - 22:28

List Question

All $n$ such that $n+2$ is a cube and $n-2$ is a square.

A problem from Observations on Arithmetica

Solve $2^x+y^2=z!$

If the equation $x^2 = (2^{2^y} + 1)^s + 2^t$ holds, can $t$ be odd?

$\sqrt{2^2} = 2$, $\sqrt{2^4} = 2^2 = 4$, $\sqrt{2^6} = 8 \neq 6$, $\ldots$

When does $p^s = 2^t + 1$ have a solution, for $t$ odd and $p$ prime?

$\sum_1^I a_i 2^i + \sum_1^J b_j 3^j = \sum_1^I c_i 2^i + \sum_1^J d_j 3^j$

Is this an uncomputable function?

Reciprocal Solution to the Ramberg Osgood Equation

Fundamental solutions of the positive Pell Equation

Prove that the equation $x^3 + 117y^3 = 5 $ has no integer solution $x, y$

On the square values of a certain polynomial

Find all integers $x$ and $y$ such that $4y^2=x^7+1$

Why are the minimal solutions of the Pell equation $x^2-(n^2-3)y^2=1$ larger than average when $3 \not | n$?

calculate the sum of 5 numbers, knowing the product of their values minus 4

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