Question

Prove-idea for writing an odd prime number as a difference of two square-numbers

score 213 · Answer 1 · 2018-01-11 12:21:10

213

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Prove-idea for writing an odd prime number as a difference of two square-numbers

Published on 11 Jan 2018 - 12:21

score 408 · Answer 2 · 2018-01-11 16:59:28

408

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$N$-th number divisible by a perfect square

Published on 11 Jan 2018 - 16:59

score 1.8k · Answer 3 · 2018-01-11 17:14:15

1.8k

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Triangular Numbers and Perfect Squares

Published on 11 Jan 2018 - 17:14

score 8.1k · Answer 4 · 2010-10-26 16:32:56

8.1k

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$n!+1$ being a perfect square

Published on 26 Oct 2010 - 16:32

score 17.6k · Answer 5 · 2010-11-30 22:35:36

17.6k

Views

Can $n!$ be a perfect square when $n$ is an integer greater than $1$?

Published on 30 Nov 2010 - 22:35

score 5.2k · Answer 6 · 2011-02-09 23:52:09

5.2k

Views

Show that every $n$ can be written uniquely in the form $n = ab$, with $a$ square-free and $b$ a perfect square

Published on 09 Feb 2011 - 23:52

score 71.4k · Answer 7 · 2011-03-22 05:18:02

71.4k

Views

Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer

Published on 22 Mar 2011 - 5:18

score 2.5k · Answer 8 · 2011-07-09 18:10:52

2.5k

Views

Questions on perfect squares

Published on 09 Jul 2011 - 18:10

score 2k · Answer 9 · 2026-03-29 19:17:35

2k

Views

The sum of the first $n$ squares is a square: a system of two Pell-type-equations

Published on 29 Mar 2026 - 19:17

score 7.4k · Answer 10 · 2012-05-02 04:01:20

7.4k

Views

Prove that every positive integer $n$ is a unique product of a square and a squarefree number

Published on 02 May 2012 - 4:01

score 18.6k · Answer 11 · 2012-05-17 18:19:25

18.6k

Views

If $n$ is an odd natural number, then $8$ divides $n^{2}-1$

Published on 17 May 2012 - 18:19

score 714 · Answer 12 · 2026-03-29 19:16:00

714

Views

Finding all integers such that $a^2+4b^2 , 4a^2+b^2$ are both perfect squares

Published on 29 Mar 2026 - 19:16

score 117 · Answer 13 · 2012-10-01 12:13:45

117

Views

Solving $x!+1=y^2 $integer solutions,example：$(4,5),(5,11),(7,71)$

Published on 01 Oct 2012 - 12:13

score 15.6k · Answer 14 · 2013-01-23 00:34:10

15.6k

Views

If a and b are relatively prime and ab is a square, then a and b are squares.

Published on 23 Jan 2013 - 0:34

score 21.6k · Answer 15 · 2026-02-23 12:06:36

21.6k

Views

Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer

Published on 23 Feb 2026 - 12:06

List Question

Prove-idea for writing an odd prime number as a difference of two square-numbers

$N$-th number divisible by a perfect square

Triangular Numbers and Perfect Squares

$n!+1$ being a perfect square

Can $n!$ be a perfect square when $n$ is an integer greater than $1$?

Show that every $n$ can be written uniquely in the form $n = ab$, with $a$ square-free and $b$ a perfect square

Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer

Questions on perfect squares

The sum of the first $n$ squares is a square: a system of two Pell-type-equations

Prove that every positive integer $n$ is a unique product of a square and a squarefree number

If $n$ is an odd natural number, then $8$ divides $n^{2}-1$

Finding all integers such that $a^2+4b^2 , 4a^2+b^2$ are both perfect squares

Solving $x!+1=y^2 $integer solutions,example：$(4,5),(5,11),(7,71)$

If a and b are relatively prime and ab is a square, then a and b are squares.

Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer

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