Question

If $m$ and $n$ are relatively prime positive integers, prove that $m^{\phi(n)}+n^{\phi(m)}\equiv1\pmod{mn}$

score 3.8k · Answer 1 · 2018-11-15 20:51:26

3.8k

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If $m$ and $n$ are relatively prime positive integers, prove that $m^{\phi(n)}+n^{\phi(m)}\equiv1\pmod{mn}$

Published on 15 Nov 2018 - 20:51

score 45 · Answer 2 · 2018-11-15 21:54:30

45

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How to show $2l+1\equiv (2l+1)^{4n+1}\pmod{5}, \forall l$ in the integers?

Published on 15 Nov 2018 - 21:54

score 25 · Answer 3 · 2018-11-16 01:53:15

25

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finding m for which modular arithmetic statement is true

Published on 16 Nov 2018 - 1:53

score 116 · Answer 4 · 2018-11-16 04:12:07

116

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Congruence with algebraic exponents

Published on 16 Nov 2018 - 4:12

score 229 · Answer 5 · 2026-03-25 06:09:01

229

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Integer solutions of a variable coefficient polynomial

Published on 25 Mar 2026 - 6:09

score 117 · Answer 6 · 2026-03-27 01:44:57

117

Views

Prove that $2005|\underbrace{55 \ldots5}_{800\text{ digits}}$

Published on 27 Mar 2026 - 1:44

score 294 · Answer 7 · 2026-03-25 06:09:11

294

Views

Visualizing rational numbers as multiplication graphs

Published on 25 Mar 2026 - 6:09

score 91 · Answer 8 · 2018-11-16 15:54:31

Show that: $a·c \equiv b·c\ (\text{mod }m)$ with $a, b, c$ and $m$ integers with $m \ge 2$ does not imply $a \equiv b\ (\text{mod }m)$

score 114 · Answer 9 · 2026-03-27 06:51:29

114

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Fermat-Catalan eighth powers

Published on 27 Mar 2026 - 6:51

score 152 · Answer 10 · 2018-11-16 20:54:59

152

Views

Proof that Sylvester numbers, when reduced modulo 864 , form an arithmetic progression 7,43,79,115,151,187,223,…

Published on 16 Nov 2018 - 20:54

score 90 · Answer 11 · 2018-11-17 10:02:40

90

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Find a Matrix A on the ring of integers modulo 3 so that KerA=ImB.

Published on 17 Nov 2018 - 10:02

score 545 · Answer 12 · 2018-11-17 16:46:48

545

Views

Modulo operation for integers and reals?

Published on 17 Nov 2018 - 16:46

score 450 · Answer 13 · 2026-03-28 05:20:50

450

Views

A mod 2 binomial identity

Published on 28 Mar 2026 - 5:20

score 23 · Answer 14 · 2018-11-17 18:45:38

23

Views

Additive bijection between module sets.

Published on 17 Nov 2018 - 18:45

score 136 · Answer 15 · 2018-11-18 10:52:53

136

Views

Show that there exists infinitely many primes which satisfy a given congurence.

Published on 18 Nov 2018 - 10:52

List Question

If $m$ and $n$ are relatively prime positive integers, prove that $m^{\phi(n)}+n^{\phi(m)}\equiv1\pmod{mn}$

How to show $2l+1\equiv (2l+1)^{4n+1}\pmod{5}, \forall l$ in the integers?

finding m for which modular arithmetic statement is true

Congruence with algebraic exponents

Integer solutions of a variable coefficient polynomial

Prove that $2005|\underbrace{55 \ldots5}_{800\text{ digits}}$

Visualizing rational numbers as multiplication graphs

Show that: $a·c \equiv b·c\ (\text{mod }m)$ with $a, b, c$ and $m$ integers with $m \ge 2$ does not imply $a \equiv b\ (\text{mod }m)$

Fermat-Catalan eighth powers

Proof that Sylvester numbers, when reduced modulo 864 , form an arithmetic progression 7,43,79,115,151,187,223,…

Find a Matrix A on the ring of integers modulo 3 so that KerA=ImB.

Modulo operation for integers and reals?

A mod 2 binomial identity

Additive bijection between module sets.

Show that there exists infinitely many primes which satisfy a given congurence.

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