Question

Show that exist infinitely many pairs of natural numbers $(m, n)$ such that $\text{gcd}(m^2+1, n^2+1)=m+n$.

score 620 · Answer 1 · 2026-03-29 12:39:21

620

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Show that exist infinitely many pairs of natural numbers $(m, n)$ such that $\text{gcd}(m^2+1, n^2+1)=m+n$.

Published on 29 Mar 2026 - 12:39

score 204 · Answer 2 · 2016-10-08 15:39:08

204

Views

Divisibility When Adding One per Day

Published on 08 Oct 2016 - 15:39

score 869 · Answer 3 · 2016-10-08 18:49:44

869

Views

Divisibility Proof $8\mid (x^2 - y^2)$ for $x$ and $y$ odd

Published on 08 Oct 2016 - 18:49

score 98 · Answer 4 · 2016-10-09 04:00:58

98

Views

If $\nexists d \in \mathbb{N}: 1<d<\sqrt{n}$, then $n$ is prime

Published on 09 Oct 2016 - 4:00

score 136 · Answer 5 · 2016-10-09 04:32:39

136

Views

How to correctly prove whether $\exists x \in \mathbb{Z}: x^{2} \equiv 43 (\mod 9999)$

Published on 09 Oct 2016 - 4:32

score 574 · Answer 6 · 2026-03-30 05:36:31

574

Views

Proof about divisibility and greatest common divisor that doesn't use Bezout's formula

Published on 30 Mar 2026 - 5:36

score 120 · Answer 7 · 2026-03-31 13:10:24

120

Views

Show that $p^{n-1}$ does not divide $k!$, with $p$ an odd prime, $n>1$ and $0<k<n$.

Published on 31 Mar 2026 - 13:10

score 621 · Answer 8 · 2016-10-09 17:54:37

621

Views

Rules of thumb for divisibility

Published on 09 Oct 2016 - 17:54

score 281 · Answer 9 · 2026-03-30 05:36:30

281

Views

Why do $g'|g$ and $g|g'$, when $g=\gcd(a,b)$ and $g'=\gcd(a,b)$?

Published on 30 Mar 2026 - 5:36

score 372 · Answer 10 · 2016-10-09 23:07:26

372

Views

Describe all natural numbers $n$ for which $3^{n}-2^{n}$ is divisible by $5$.

Published on 09 Oct 2016 - 23:07

score 109 · Answer 11 · 2016-10-10 19:28:40

109

Views

If $n\mid m$ and $m\mid r$, then $n\mid(r+r^2)$

Published on 10 Oct 2016 - 19:28

score 820 · Answer 12 · 2026-03-30 03:21:33

820

Views

Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime

Published on 30 Mar 2026 - 3:21

score 84 · Answer 13 · 2016-10-10 20:33:52

84

Views

$a^{n+1} + 2^{n+1} + 1$ is divisible with $a^n + 2^n + 1$, find $a$

Published on 10 Oct 2016 - 20:33

score 54 · Answer 14 · 2016-10-10 20:59:13

54

Views

Prove $p$ has only $2$ divisors: $1$ and $p$

Published on 10 Oct 2016 - 20:59

score 523 · Answer 15 · 2016-10-11 00:17:08

523

Views

how many of the resulting number are divisible by 11 but not by 5?

Published on 11 Oct 2016 - 0:17

List Question

Show that exist infinitely many pairs of natural numbers $(m, n)$ such that $\text{gcd}(m^2+1, n^2+1)=m+n$.

Divisibility When Adding One per Day

Divisibility Proof $8\mid (x^2 - y^2)$ for $x$ and $y$ odd

If $\nexists d \in \mathbb{N}: 1<d<\sqrt{n}$, then $n$ is prime

How to correctly prove whether $\exists x \in \mathbb{Z}: x^{2} \equiv 43 (\mod 9999)$

Proof about divisibility and greatest common divisor that doesn't use Bezout's formula

Show that $p^{n-1}$ does not divide $k!$, with $p$ an odd prime, $n>1$ and $0<k<n$.

Rules of thumb for divisibility

Why do $g'|g$ and $g|g'$, when $g=\gcd(a,b)$ and $g'=\gcd(a,b)$?

Describe all natural numbers $n$ for which $3^{n}-2^{n}$ is divisible by $5$.

If $n\mid m$ and $m\mid r$, then $n\mid(r+r^2)$

Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime

$a^{n+1} + 2^{n+1} + 1$ is divisible with $a^n + 2^n + 1$, find $a$

Prove $p$ has only $2$ divisors: $1$ and $p$

how many of the resulting number are divisible by 11 but not by 5?

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