List questions from elementary-number-theory

Published on 16 Apr 2026 - 18:23

77

Views

Proof that this map is well-defined $ \phi(a \bmod{mn})= (a \bmod m, a \bmod n) $

Published on 14 Apr 2026 - 13:04

150

Views

Show that an Affine Cipher with a prime modulo $N$ fixes exactly one plaintext message $m$ in $\mathcal M$

Published on 14 Apr 2026 - 14:04

74

Views

What proof proves that given any number, when dividing by two recursively, you will always reach 1?

Published on 14 Apr 2026 - 7:10

407

Views

Counting kth power residues mod $p^a$

Published on 12 Apr 2026 - 6:26

100

Views

Fermat's Little Theorem and solving $n^2 \equiv -1 \pmod p$

Published on 06 May 2026 - 2:41

2.1k

Views

Proving multiplicative inverse of modulo $m$ exists when $\gcd(m,x)=1$

Published on 17 Apr 2026 - 2:48

2.7k

Views

Could prime numbers be defined like this?

Published on 15 Apr 2026 - 8:41

81

Views

Recursive Induction Problem

Published on 11 Apr 2026 - 3:59

70

Views

Decrypting an Affine Cipher $ e(m)=am+b\pmod{27}$ knowing $e(8)\equiv 14$ and $e(26)\equiv 5$

Published on 15 Apr 2026 - 23:50

77

Views

Solution for $2^n = 12k$

Published on 13 Apr 2026 - 23:55

92

Views

Adding to the denominator of two fractions

Published on 10 Apr 2026 - 17:51

60

Views

Prove true by using induction

Published on 13 Apr 2026 - 17:27

74

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$gcd(i,n)=1 \iff n\nmid ik$ for all $1 \leq k \leq n-1$

Published on 16 Apr 2026 - 14:47

158

Views

Solving Diophantine equation without brute force

Published on 12 Apr 2026 - 23:18

List Question

If $a^b\equiv a^c\equiv 1\pmod{m}$ and $g=\gcd(b,c)$ prove $a^g\equiv 1\pmod{m}$

Proof that this map is well-defined $ \phi(a \bmod{mn})= (a \bmod m, a \bmod n) $

Show that an Affine Cipher with a prime modulo $N$ fixes exactly one plaintext message $m$ in $\mathcal M$

What proof proves that given any number, when dividing by two recursively, you will always reach 1?

Counting kth power residues mod $p^a$

Fermat's Little Theorem and solving $n^2 \equiv -1 \pmod p$

Proving multiplicative inverse of modulo $m$ exists when $\gcd(m,x)=1$

Could prime numbers be defined like this?

Recursive Induction Problem

Decrypting an Affine Cipher $ e(m)=am+b\pmod{27}$ knowing $e(8)\equiv 14$ and $e(26)\equiv 5$

Solution for $2^n = 12k$

Adding to the denominator of two fractions

Prove true by using induction

$gcd(i,n)=1 \iff n\nmid ik$ for all $1 \leq k \leq n-1$

Solving Diophantine equation without brute force

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