Question

We have $a^{n-1} \equiv 1\ (mod\ n)$ but $a^{m} \not\equiv 1\ (mod\ n)$ for every divisor $m$ of $n - 1$, other than itself. Prove that $n$ is prime.

score 189 · Answer 1 · 2026-03-25 07:46:26

189

Views

We have $a^{n-1} \equiv 1\ (mod\ n)$ but $a^{m} \not\equiv 1\ (mod\ n)$ for every divisor $m$ of $n - 1$, other than itself. Prove that $n$ is prime.

Published on 25 Mar 2026 - 7:46

score 51 · Answer 2 · 2026-03-25 07:46:05

51

Views

Reducing the result of $z=e^{x^2-y^2}\cos(2xy)$ after a coordinate rotation by $45^\circ$

Published on 25 Mar 2026 - 7:46

score 358 · Answer 3 · 2026-03-25 07:44:33

358

Views

If $m > 0$, fix a reduced residue system $r_{1}, r_2, \dotsc, r_{\varphi(m)} $ mod $ m$. Let $x=r_1+r_2+\dotsb+r_{\varphi(m)}$. What is $x$ mod $m$?

Published on 25 Mar 2026 - 7:44

score 55 · Answer 4 · 2026-03-25 07:43:50

55

Views

Prove that the there exists a single Reduced residue system.

Published on 25 Mar 2026 - 7:43

score 129 · Answer 5 · 2026-03-25 07:40:58

129

Views

Primes in reduced residue systems

Published on 25 Mar 2026 - 7:40

score 1.8k · Answer 6 · 2026-03-25 07:43:38

1.8k

Views

Sum of elements in reduced residue system modulo n is divisible by n

Published on 25 Mar 2026 - 7:43

score 107 · Answer 7 · 2026-03-25 07:48:58

107

Views

Does the Sylvester-Schur theorem apply to complete residue systems?

Published on 25 Mar 2026 - 7:48

score 65 · Answer 8 · 2026-03-25 07:43:12

65

Views

This should be a reduced residue system rather than a complete residue system, right?

Published on 25 Mar 2026 - 7:43

score 225 · Answer 9 · 2026-03-25 06:11:21

225

Views

Reduced residue systems and prime k-tuple bijection

Published on 25 Mar 2026 - 6:11

score 186 · Answer 10 · 2026-03-25 09:22:46

186

Views

Reduced Residue System in Mathematica

Published on 25 Mar 2026 - 9:22

score 148 · Answer 11 · 2026-03-25 07:45:53

148

Views

Regarding proving a result related to complete residue system which is to be used in proving multiplicative property of Hecke Operators

Published on 25 Mar 2026 - 7:45

score 236 · Answer 12 · 2026-03-25 07:46:01

236

Views

Proof of infinitude of primes using ratio of n to its totient

Published on 25 Mar 2026 - 7:46

score 722 · Answer 13 · 2026-03-25 07:45:53

722

Views

The product of both quadratic residues and non residues in a residue system modulo prime p

Published on 25 Mar 2026 - 7:45

score 87 · Answer 14 · 2020-05-27 16:06:45

87

Views

Representatives of residue classes as elements of a vector space

Published on 27 May 2020 - 16:06

score 765 · Answer 15 · 2026-03-25 07:42:02

765

Views

Reduced residue system from complete residue system

Published on 25 Mar 2026 - 7:42

List Question

We have $a^{n-1} \equiv 1\ (mod\ n)$ but $a^{m} \not\equiv 1\ (mod\ n)$ for every divisor $m$ of $n - 1$, other than itself. Prove that $n$ is prime.

Reducing the result of $z=e^{x^2-y^2}\cos(2xy)$ after a coordinate rotation by $45^\circ$

If $m > 0$, fix a reduced residue system $r_{1}, r_2, \dotsc, r_{\varphi(m)} $ mod $ m$. Let $x=r_1+r_2+\dotsb+r_{\varphi(m)}$. What is $x$ mod $m$?

Prove that the there exists a single Reduced residue system.

Primes in reduced residue systems

Sum of elements in reduced residue system modulo n is divisible by n

Does the Sylvester-Schur theorem apply to complete residue systems?

This should be a reduced residue system rather than a complete residue system, right?

Reduced residue systems and prime k-tuple bijection

Reduced Residue System in Mathematica

Regarding proving a result related to complete residue system which is to be used in proving multiplicative property of Hecke Operators

Proof of infinitude of primes using ratio of n to its totient

The product of both quadratic residues and non residues in a residue system modulo prime p

Representatives of residue classes as elements of a vector space

Reduced residue system from complete residue system

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