List questions from square-numbers

Published on 29 Mar 2026 - 5:34

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When is the number $81 + 60 x (1 + x) (-2 + 5 x)$ a perfect square for $x\ge2$ and $x\in\mathbb{N}$

Published on 29 Mar 2026 - 5:34

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When does a certain number is a perfect square

Published on 29 Mar 2026 - 7:21

129

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$\frac{1}{5}\big((4 + \sqrt{15})^{2n} + (4 - \sqrt{15})^{2n} + 8\big)$ is the sum of 3 consecutive squares

Published on 03 Dec 2019 - 9:44

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Proving that a list of perfect square numbers is complete

Published on 28 Mar 2026 - 1:59

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Can any number of squares sum to a square?

Published on 23 Feb 2026 - 3:01

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Product of numbers in a set

Published on 09 Dec 2019 - 15:26

162

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444...44+2×888...88+4 is perfect square?

Published on 10 Dec 2019 - 15:26

243

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Why is $\underbrace{444\dots44}_{2n} + \underbrace{888\dots88}_{n} + 4$ never a perfect square?

Published on 10 Dec 2019 - 21:23

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Square Numbers general methods

Published on 11 Dec 2019 - 18:04

61

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Close to the integer squares ?? $ f(x) = \sum_{n=1}^{\infty} g(n)^{-x} ,f(4 n) = \zeta(8 n) $

Published on 29 Mar 2026 - 4:44

53

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Are there infinite square free integers $4x+1, 4x+2, 4x+3$

Published on 17 Dec 2019 - 17:06

586

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Find all integers $m,\ n$ such that $m^2+4n$ and $n^2+4m$ are both squares.

Published on 19 Dec 2019 - 1:13

104

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What primes $p$ satisfying $11 p+1$ to be a perfect square?

Published on 22 Dec 2019 - 22:26

125

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Finding perfect squares in a quadratic equation

Published on 24 Dec 2019 - 20:46

List Question

For what value of $x$ is the following number a perfect square

When is the number $81 + 60 x (1 + x) (-2 + 5 x)$ a perfect square for $x\ge2$ and $x\in\mathbb{N}$

When does a certain number is a perfect square

$\frac{1}{5}\big((4 + \sqrt{15})^{2n} + (4 - \sqrt{15})^{2n} + 8\big)$ is the sum of 3 consecutive squares

Proving that a list of perfect square numbers is complete

Can any number of squares sum to a square?

Product of numbers in a set

444...44+2×888...88+4 is perfect square?

Why is $\underbrace{444\dots44}_{2n} + \underbrace{888\dots88}_{n} + 4$ never a perfect square?

Square Numbers general methods

Close to the integer squares ?? $ f(x) = \sum_{n=1}^{\infty} g(n)^{-x} ,f(4 n) = \zeta(8 n) $

Are there infinite square free integers $4x+1, 4x+2, 4x+3$

Find all integers $m,\ n$ such that $m^2+4n$ and $n^2+4m$ are both squares.

What primes $p$ satisfying $11 p+1$ to be a perfect square?

Finding perfect squares in a quadratic equation

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