List questions from square-numbers

Published on 23 Apr 2017 - 9:07

266

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Suppose $x$ is a perfect square mod $n$. If $xy \equiv 1 $ mod $n$, prove $y$ is a perfect square also.

Published on 26 Apr 2017 - 2:27

1.7k

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If $ab$ is a square number and $\gcd(a,b) = 1$, then $a$ and $b$ are square numbers.

Published on 26 Apr 2017 - 23:31

484

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For how many numbers $X^2 \equiv X \mod 10^n$?

Published on 28 Apr 2017 - 0:38

110

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Are there three integers such the nontrivial sums are squares and three are squares of consecutives?

Published on 30 Apr 2017 - 13:44

2.9k

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Square root of k

Published on 02 May 2017 - 15:31

323

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Squares in $\mathbb{Q}_p \bmod p$ (p-adic numbers)

Published on 25 Mar 2026 - 7:41

12.2k

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A number that is a triangle number and also a square number.

Published on 05 May 2017 - 15:52

35

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Square numbers ???

Published on 07 May 2017 - 11:51

57

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$x$ is a positive integer with at least 2 digits, a perfect square, and its tens digit is odd. What are the possible units digits of x?

Published on 01 Apr 2026 - 8:52

111

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Show that $n + (\sqrt n)$ is not a perfect square

Published on 13 May 2017 - 18:32

410

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Find, with proof, all prime numbers $p$ and $q$ such that $p^2-2q^2=1$

Published on 13 May 2017 - 20:34

55

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Every polynomial that takes square values is another polynomial squared

Published on 23 May 2017 - 18:54

393

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What does "turn into a perfect square" mean here?

Published on 24 May 2017 - 16:46

3.5k

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How to compute 2-adic square roots?

Published on 26 Mar 2026 - 12:42

List Question

Can 40 divide n with the following conditions

Suppose $x$ is a perfect square mod $n$. If $xy \equiv 1 $ mod $n$, prove $y$ is a perfect square also.

If $ab$ is a square number and $\gcd(a,b) = 1$, then $a$ and $b$ are square numbers.

For how many numbers $X^2 \equiv X \mod 10^n$?

Are there three integers such the nontrivial sums are squares and three are squares of consecutives?

Square root of k

Squares in $\mathbb{Q}_p \bmod p$ (p-adic numbers)

A number that is a triangle number and also a square number.

Square numbers ???

$x$ is a positive integer with at least 2 digits, a perfect square, and its tens digit is odd. What are the possible units digits of x?

Show that $n + (\sqrt n)$ is not a perfect square

Find, with proof, all prime numbers $p$ and $q$ such that $p^2-2q^2=1$

Every polynomial that takes square values is another polynomial squared

What does "turn into a perfect square" mean here?

How to compute 2-adic square roots?

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