Question

Proof of $g^a \equiv 1 \pmod{m}$ and $g^b \equiv 1 \pmod{m} \quad \implies \quad g^{\gcd(a,b)} \equiv 1 \pmod{m}$

score 1.3k · Answer 1 · 2026-03-31 21:02:05

1.3k

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Proof of $g^a \equiv 1 \pmod{m}$ and $g^b \equiv 1 \pmod{m} \quad \implies \quad g^{\gcd(a,b)} \equiv 1 \pmod{m}$

Published on 31 Mar 2026 - 21:02

score 139 · Answer 2 · 2014-09-15 06:07:21

139

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Exists an explicit formula to calculate the minimum $n$ for some $x$ such that $\frac{x}{2^n}\in[0,0.5)+\Bbb Z$?

Published on 15 Sep 2014 - 6:07

score 206 · Answer 3 · 2026-03-27 03:41:42

206

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$A^{-1}x \pmod{26}$ and coprime requirement in Hill cipher

Published on 27 Mar 2026 - 3:41

score 220 · Answer 4 · 2026-04-07 20:53:45

220

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CRT Algorithm using InvMod + Undefined

Published on 07 Apr 2026 - 20:53

score 2.1k · Answer 5 · 2014-09-17 09:09:55

2.1k

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Modular nth roots, e.g. $x^5 \equiv 6 \pmod{31}$

Published on 17 Sep 2014 - 9:09

score 1.7k · Answer 6 · 2014-09-17 13:50:39

1.7k

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Find the remainder when $2^{561}$ is divided by $561$ using simple congruence properties.

Published on 17 Sep 2014 - 13:50

score 91 · Answer 7 · 2014-09-17 14:16:10

91

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Congruences in number theory

Published on 17 Sep 2014 - 14:16

score 74 · Answer 8 · 2014-09-18 18:59:24

74

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If there is a subset with sum divisible by n, then take out an integer of the subset. How many moves?

Published on 18 Sep 2014 - 18:59

score 107 · Answer 9 · 2014-09-18 21:27:33

107

Views

Why is any number to the 1,5,9,13, etc. modulus 10 itself?

Published on 18 Sep 2014 - 21:27

score 136 · Answer 10 · 2026-03-27 08:38:52

136

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The modular n-th root (mod p*q)

Published on 27 Mar 2026 - 8:38

score 59 · Answer 11 · 2026-03-26 06:25:47

59

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Explanation of congruence and modulo

Published on 26 Mar 2026 - 6:25

score 1.1k · Answer 12 · 2014-09-21 01:05:22

1.1k

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Simplifying a proof by contradiction: if $a\equiv 1\bmod 5$, then $a^2\equiv 1\bmod5$

Published on 21 Sep 2014 - 1:05

score 56 · Answer 13 · 2014-09-21 04:09:33

56

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[ANSWERED]Is $\{n, n^{2} n^{3}\}$ a group under multiplication modulo $m = n + n^{2} + n^{3}$?

Published on 21 Sep 2014 - 4:09

score 84 · Answer 14 · 2014-09-21 09:37:09

84

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Proof of Little Fermat's Theorem for a=7

Published on 21 Sep 2014 - 9:37

score 1.7k · Answer 15 · 2014-09-22 07:35:33

1.7k

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The number $2^{29}$ has $9$ distinct digits. Find the missing digit without the use of a calculator.

Published on 22 Sep 2014 - 7:35

List Question

Proof of $g^a \equiv 1 \pmod{m}$ and $g^b \equiv 1 \pmod{m} \quad \implies \quad g^{\gcd(a,b)} \equiv 1 \pmod{m}$

Exists an explicit formula to calculate the minimum $n$ for some $x$ such that $\frac{x}{2^n}\in[0,0.5)+\Bbb Z$?

$A^{-1}x \pmod{26}$ and coprime requirement in Hill cipher

CRT Algorithm using InvMod + Undefined

Modular nth roots, e.g. $x^5 \equiv 6 \pmod{31}$

Find the remainder when $2^{561}$ is divided by $561$ using simple congruence properties.

Congruences in number theory

If there is a subset with sum divisible by n, then take out an integer of the subset. How many moves?

Why is any number to the 1,5,9,13, etc. modulus 10 itself?

The modular n-th root (mod p*q)

Explanation of congruence and modulo

Simplifying a proof by contradiction: if $a\equiv 1\bmod 5$, then $a^2\equiv 1\bmod5$

[ANSWERED]Is $\{n, n^{2} n^{3}\}$ a group under multiplication modulo $m = n + n^{2} + n^{3}$?

Proof of Little Fermat's Theorem for a=7

The number $2^{29}$ has $9$ distinct digits. Find the missing digit without the use of a calculator.

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