Question

Why must the $gcd((N-1)!,N)=1$ in order to factor out $(N-1)!$ from both sides of $a^{N-1}(N-1)! \equiv (N-1)! \pmod N $?

score 61 · Answer 1 · 2019-08-03 14:34:38

61

Views

Why must the $gcd((N-1)!,N)=1$ in order to factor out $(N-1)!$ from both sides of $a^{N-1}(N-1)! \equiv (N-1)! \pmod N $?

Published on 03 Aug 2019 - 14:34

score 188 · Answer 2 · 2026-03-26 06:04:12

188

Views

Can a quotient space be defined using a set that is not closed

Published on 26 Mar 2026 - 6:04

score 368 · Answer 3 · 2019-08-05 16:38:01

368

Views

Modular arithmetic. $(-1)^rr! \equiv 1 \pmod p$, then $(p-r-1)! \equiv -1 \pmod p$

Published on 05 Aug 2019 - 16:38

score 104 · Answer 4 · 2019-08-06 02:39:16

104

Views

Meaning of congruence (in twin prime criterion)

Published on 06 Aug 2019 - 2:39

score 104 · Answer 5 · 2019-08-05 19:03:40

104

Views

How to solve inverse modulo?

Published on 05 Aug 2019 - 19:03

score 127 · Answer 6 · 2019-08-06 15:51:16

127

Views

Is this limit for the sum of remainders correct?

Published on 06 Aug 2019 - 15:51

score 181 · Answer 7 · 2019-08-06 18:33:01

181

Views

Modular arithmetic $(2n+1)x \equiv -7 \pmod 9$

Published on 06 Aug 2019 - 18:33

score 62 · Answer 8 · 2026-03-28 14:55:19

62

Views

Find the modular inverse of a number when $b\neq1$

Published on 28 Mar 2026 - 14:55

score 1.5k · Answer 9 · 2026-03-25 20:32:41

1.5k

Views

How can one prove a recognized modulo pattern?

Published on 25 Mar 2026 - 20:32

score 214 · Answer 10 · 2019-08-07 16:30:03

214

Views

Modular arithmetic $(3n - 2)x + 5n \equiv 0 \pmod{9n-9}$

Published on 07 Aug 2019 - 16:30

score 85 · Answer 11 · 2026-03-28 14:56:51

85

Views

Find the inverse in $F = \frac{\Bbb{Z}_{7}[x]}{g(x)}$ of a polynomial $p(x)$

Published on 28 Mar 2026 - 14:56

score 1.4k · Answer 12 · 2019-08-07 20:20:57

1.4k

Views

solving a function where [x mod y represents the remainder after division of x by y]

Published on 07 Aug 2019 - 20:20

score 123 · Answer 13 · 2019-08-08 09:37:07

123

Views

Prove that the ring $\mathbb{Z}_n$ contains a nonzero element $a$, such that $a^2=0$ if and only if $p^2|n$ for some prime p

Published on 08 Aug 2019 - 9:37

score 98 · Answer 14 · 2019-08-08 23:03:36

98

Views

For the set $ S=\{0, 1, 2, ...., n-1\}$, count the number of times that $(n) \vert (ab-cd)$

Published on 08 Aug 2019 - 23:03

score 928 · Answer 15 · 2019-08-09 02:57:38

928

Views

How dense are primes congruent to 1 and 3 (mod 4)?

Published on 09 Aug 2019 - 2:57

List Question

Why must the $gcd((N-1)!,N)=1$ in order to factor out $(N-1)!$ from both sides of $a^{N-1}(N-1)! \equiv (N-1)! \pmod N $?

Can a quotient space be defined using a set that is not closed

Modular arithmetic. $(-1)^rr! \equiv 1 \pmod p$, then $(p-r-1)! \equiv -1 \pmod p$

Meaning of congruence (in twin prime criterion)

How to solve inverse modulo?

Is this limit for the sum of remainders correct?

Modular arithmetic $(2n+1)x \equiv -7 \pmod 9$

Find the modular inverse of a number when $b\neq1$

How can one prove a recognized modulo pattern?

Modular arithmetic $(3n - 2)x + 5n \equiv 0 \pmod{9n-9}$

Find the inverse in $F = \frac{\Bbb{Z}_{7}[x]}{g(x)}$ of a polynomial $p(x)$

solving a function where [x mod y represents the remainder after division of x by y]

Prove that the ring $\mathbb{Z}_n$ contains a nonzero element $a$, such that $a^2=0$ if and only if $p^2|n$ for some prime p

For the set $ S=\{0, 1, 2, ...., n-1\}$, count the number of times that $(n) \vert (ab-cd)$

How dense are primes congruent to 1 and 3 (mod 4)?

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