List questions from square-numbers

Published on 24 Feb 2015 - 12:59

98

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Application: Sum of Digits

Published on 28 Mar 2026 - 23:10

2.4k

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Arrangement of integers in a row such that the sum of every two adjacent numbers is a perfect square.

Published on 28 Feb 2015 - 15:33

2.6k

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Prove that there is no perfect square that is congruent to 2 mod 10 and 3 mod 10.

Published on 29 Mar 2026 - 4:26

199

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When is $20q^4-40q^3+30q^2-10q$ a square for positive integer $q$?

Published on 04 Mar 2015 - 21:53

63

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Is $8r+1$ always a square for integer $r$?

Published on 05 Mar 2015 - 18:52

57

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When is this sequence of positive integers a square?

Published on 05 Mar 2015 - 20:17

259

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Is there a primality test based on the sum of squares of the first $n$ natural numbers $\sum_{x = 1}^{n} x^2$?

Published on 27 Mar 2026 - 0:10

699

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A prime number generator algorithm based on $x^2+(x-1)^2$ that generates only primes

Published on 29 Mar 2026 - 6:04

407

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Show that $m+3$ and $m^2 + 3m +3$ cannot both be perfect cubes.

Published on 15 Mar 2015 - 15:28

593

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How do I prove that $3^n - 3$ is never a square number?

Published on 26 Mar 2026 - 4:32

3.1k

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How to determine what numbers are perfect squares without calculator?

Published on 19 Mar 2015 - 1:05

214

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The smallest $n$ for which $19n+1$ and $95n+1$ are perfect squares

Published on 19 Mar 2015 - 12:54

85

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What are the properties of the positive real numbers pair $(a,b)$ for which $a b \geq a + b$?

Published on 21 Mar 2015 - 6:04

628

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Proving an expression is perfect square

Published on 23 Mar 2015 - 18:00

List Question

when is $n!+10$ a perfect square?

Application: Sum of Digits

Arrangement of integers in a row such that the sum of every two adjacent numbers is a perfect square.

Prove that there is no perfect square that is congruent to 2 mod 10 and 3 mod 10.

When is $20q^4-40q^3+30q^2-10q$ a square for positive integer $q$?

Is $8r+1$ always a square for integer $r$?

When is this sequence of positive integers a square?

Is there a primality test based on the sum of squares of the first $n$ natural numbers $\sum_{x = 1}^{n} x^2$?

A prime number generator algorithm based on $x^2+(x-1)^2$ that generates only primes

Show that $m+3$ and $m^2 + 3m +3$ cannot both be perfect cubes.

How do I prove that $3^n - 3$ is never a square number?

How to determine what numbers are perfect squares without calculator?

The smallest $n$ for which $19n+1$ and $95n+1$ are perfect squares

What are the properties of the positive real numbers pair $(a,b)$ for which $a b \geq a + b$?

Proving an expression is perfect square

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