Question

$m$ and $n$ are odd numbers such that $|m^2 - n^2 + 1| \mid (n^2 - 1)$. Prove that $|m^2 - n^2 + 1|$ is a square number.

score 53 · Answer 1 · 2019-09-03 14:52:58

53

Views

$m$ and $n$ are odd numbers such that $|m^2 - n^2 + 1| \mid (n^2 - 1)$. Prove that $|m^2 - n^2 + 1|$ is a square number.

Published on 03 Sep 2019 - 14:52

score 102 · Answer 2 · 2019-09-05 01:17:49

102

Views

Prove that $3(p^2)+61$ is a perfect square only for $p = 1$

Published on 05 Sep 2019 - 1:17

score 145 · Answer 3 · 2019-09-06 04:02:33

145

Views

Prove that $(a+b)$ is a perfect square.

Published on 06 Sep 2019 - 4:02

score 86 · Answer 4 · 2019-09-07 07:24:48

86

Views

Problem about 4 prime numbers and square numbers

Published on 07 Sep 2019 - 7:24

score 237 · Answer 5 · 2019-09-10 04:14:15

237

Views

Find four rational numbers $~\frac{p}{q}~$ with $~\left|\sqrt 2 - \frac{p}{q}\right| \le \frac{1}{q^2}~$

Published on 10 Sep 2019 - 4:14

score 80 · Answer 6 · 2019-09-11 10:57:06

80

Views

Determining number of integer solutions for expression of perfect square

Published on 11 Sep 2019 - 10:57

score 450 · Answer 7 · 2026-03-26 21:27:16

450

Views

Sum of digits of squares of a number and its reverse

Published on 26 Mar 2026 - 21:27

score 110 · Answer 8 · 2019-09-13 19:55:58

110

Views

Positive integer solutions to $ p+q^{n}=x^2$

Published on 13 Sep 2019 - 19:55

score 85 · Answer 9 · 2019-09-15 07:22:19

85

Views

Determine the integers $m$ such that $1+2+3+....m=$ a perfect square

Published on 15 Sep 2019 - 7:22

score 270 · Answer 10 · 2026-03-26 17:52:55

270

Views

Sequences where $\sum\limits_{n=k}^{\infty}{a_n}=\sum\limits_{n=k}^{\infty}{a_n^2}$

Published on 26 Mar 2026 - 17:52

score 189 · Answer 11 · 2019-09-21 07:17:50

189

Views

Find all $n$ for which $3n^2+3n+1$ is a perfect square.

Published on 21 Sep 2019 - 7:17

score 1.6k · Answer 12 · 2019-09-22 06:25:56

1.6k

Views

Sum of squares of 3 consecutive numbers is not a perfect square

Published on 22 Sep 2019 - 6:25

score 79 · Answer 13 · 2019-09-25 05:47:25

79

Views

Roots of x inside square root

Published on 25 Sep 2019 - 5:47

score 75 · Answer 14 · 2026-03-26 21:35:23

75

Views

For what values of $a$ does $b\in\mathbb{N}$?

Published on 26 Mar 2026 - 21:35

score 1.8k · Answer 15 · 2014-03-12 20:37:29

1.8k

Views

Square numbers multiplied by non-square numbers

Published on 12 Mar 2014 - 20:37

List Question

$m$ and $n$ are odd numbers such that $|m^2 - n^2 + 1| \mid (n^2 - 1)$. Prove that $|m^2 - n^2 + 1|$ is a square number.

Prove that $3(p^2)+61$ is a perfect square only for $p = 1$

Prove that $(a+b)$ is a perfect square.

Problem about 4 prime numbers and square numbers

Find four rational numbers $~\frac{p}{q}~$ with $~\left|\sqrt 2 - \frac{p}{q}\right| \le \frac{1}{q^2}~$

Determining number of integer solutions for expression of perfect square

Sum of digits of squares of a number and its reverse

Positive integer solutions to $ p+q^{n}=x^2$

Determine the integers $m$ such that $1+2+3+....m=$ a perfect square

Sequences where $\sum\limits_{n=k}^{\infty}{a_n}=\sum\limits_{n=k}^{\infty}{a_n^2}$

Find all $n$ for which $3n^2+3n+1$ is a perfect square.

Sum of squares of 3 consecutive numbers is not a perfect square

Roots of x inside square root

For what values of $a$ does $b\in\mathbb{N}$?

Square numbers multiplied by non-square numbers

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