List questions from square-numbers

Published on 28 Dec 2019 - 14:42

50

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When does a right triangle with integral perimeter and area have rational sides?

Published on 30 Dec 2019 - 5:17

41

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Square rooting results

Published on 05 Jan 2020 - 21:50

669

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For any $k \gt 1$, if $n!+k$ is a square then will $n \le k$ always be true?

Published on 26 Mar 2026 - 21:27

593

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Proof of the square root method by long division

Published on 08 Jan 2020 - 11:33

162

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Find perfect square ends with 9009

Published on 10 Jan 2020 - 15:11

137

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Mathematical shortcut to determine if a number is a integer

Published on 10 Jan 2020 - 15:45

182

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Show all ways 365 can be written as the sum of 2 or more different perfect square numbers?

Published on 16 Jan 2020 - 19:17

353

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Proof that $a^2 + b^2 + ab$ and $a^2 + b^2 - ab$ can not both be perfect squares

Published on 17 Jan 2020 - 18:14

452

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A generalization of the (in)famous IMO 1988 problem 6: If $\frac{a^2 + b^2 - abc}{ab + 1}$ is a positive integer then it is a square.

Published on 20 Jan 2020 - 11:22

60

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Digits & Squares

Published on 29 Mar 2026 - 4:50

169

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Prove that $A^2=a_1^2+a_2^2-a_3^2-a_4^2$ for all integers $A$.

Published on 27 Mar 2026 - 9:48

36

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gnomes and lights vs. sieve of Eratosthenes

Published on 22 Jan 2020 - 7:34

301

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

Published on 22 Mar 2026 - 15:05

155

Views

Square numbers and divisibility

Published on 28 Jan 2020 - 20:31

List Question

Sum of "positive" numbers

When does a right triangle with integral perimeter and area have rational sides?

Square rooting results

For any $k \gt 1$, if $n!+k$ is a square then will $n \le k$ always be true?

Proof of the square root method by long division

Find perfect square ends with 9009

Mathematical shortcut to determine if a number is a integer

Show all ways 365 can be written as the sum of 2 or more different perfect square numbers?

Proof that $a^2 + b^2 + ab$ and $a^2 + b^2 - ab$ can not both be perfect squares

A generalization of the (in)famous IMO 1988 problem 6: If $\frac{a^2 + b^2 - abc}{ab + 1}$ is a positive integer then it is a square.

Digits & Squares

Prove that $A^2=a_1^2+a_2^2-a_3^2-a_4^2$ for all integers $A$.

gnomes and lights vs. sieve of Eratosthenes

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

Square numbers and divisibility

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