Question

Find $x$ in $1!+2!+\ldots+100!\equiv x \pmod{19}$

score 102 · Answer 1 · 2016-07-12 19:36:17

102

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Find $x$ in $1!+2!+\ldots+100!\equiv x \pmod{19}$

Published on 12 Jul 2016 - 19:36

score 139 · Answer 2 · 2016-07-13 13:48:03

139

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What is a generalised solution for the Chinese Remainder Theorem?

Published on 13 Jul 2016 - 13:48

score 30 · Answer 3 · 2016-07-14 17:02:55

30

Views

Construct a function pertaining to the OEIS sequence A131229 (Numbers congruent to {1,7} mod 10)

Published on 14 Jul 2016 - 17:02

score 191 · Answer 4 · 2016-07-16 17:23:18

191

Views

Prove that $\sum^{n-1}_{i=1}i^{(n-1)} \equiv -1$ (mod $n$) for all prime $n\in\mathbb{N}$.

Published on 16 Jul 2016 - 17:23

score 2.2k · Answer 5 · 2016-07-16 21:01:02

2.2k

Views

Solving linear congruences with unknown modulus

Published on 16 Jul 2016 - 21:01

score 53 · Answer 6 · 2016-07-18 13:04:38

53

Views

For which $0\leq a<p^2$, where $p$ is an odd prime, we have that $(2p-1)!\equiv a\mod{p^2}$

Published on 18 Jul 2016 - 13:04

score 59 · Answer 7 · 2026-03-25 09:15:39

59

Views

Why does an even $x$ imply $y^2=-2 \pmod 8$

Published on 25 Mar 2026 - 9:15

score 1k · Answer 8 · 2016-07-19 20:01:28

1k

Views

How many solutions of $\mod 63$ : $x^2=1 \pmod7 $ and $x^3=1\pmod 9$

Published on 19 Jul 2016 - 20:01

score 35 · Answer 9 · 2016-07-20 09:51:25

35

Views

$i \equiv k \mod p \implies i = k$ if $p$ is prime?

Published on 20 Jul 2016 - 9:51

score 105 · Answer 10 · 2016-07-21 20:14:55

105

Views

For all $x$ , $x^2 \equiv 0$ or $1$ or $4 \mod 7$

Published on 21 Jul 2016 - 20:14

score 1.3k · Answer 11 · 2016-07-25 00:18:17

1.3k

Views

Why is $10^k - 1$ divisible by $9$?

Published on 25 Jul 2016 - 0:18

score 276 · Answer 12 · 2016-07-25 05:17:56

276

Views

I need to find the least nonnegative residue

Published on 25 Jul 2016 - 5:17

score 1.9k · Answer 13 · 2016-07-25 17:11:37

1.9k

Views

Prove that ${2^n-1\choose k}$ and ${2^n-k\choose k}$ ar always odd.

Published on 25 Jul 2016 - 17:11

score 2.1k · Answer 14 · 2016-07-26 07:51:01

2.1k

Views

Proving $133|a^{18}-b^{18}$ if $\gcd(a,133)=\gcd(b,133)=1$.

Published on 26 Jul 2016 - 7:51

score 182 · Answer 15 · 2016-07-28 13:37:20

182

Views

Compute $5^{15}$ mod $7$ using the fact that if gcd$(a,n) = 1$, then $a^{\phi(n)}$ mod $n$ = $1$ (Euler-phi function).

Published on 28 Jul 2016 - 13:37

List Question

Find $x$ in $1!+2!+\ldots+100!\equiv x \pmod{19}$

What is a generalised solution for the Chinese Remainder Theorem?

Construct a function pertaining to the OEIS sequence A131229 (Numbers congruent to {1,7} mod 10)

Prove that $\sum^{n-1}_{i=1}i^{(n-1)} \equiv -1$ (mod $n$) for all prime $n\in\mathbb{N}$.

Solving linear congruences with unknown modulus

For which $0\leq a<p^2$, where $p$ is an odd prime, we have that $(2p-1)!\equiv a\mod{p^2}$

Why does an even $x$ imply $y^2=-2 \pmod 8$

How many solutions of $\mod 63$ : $x^2=1 \pmod7 $ and $x^3=1\pmod 9$

$i \equiv k \mod p \implies i = k$ if $p$ is prime?

For all $x$ , $x^2 \equiv 0$ or $1$ or $4 \mod 7$

Why is $10^k - 1$ divisible by $9$?

I need to find the least nonnegative residue

Prove that ${2^n-1\choose k}$ and ${2^n-k\choose k}$ ar always odd.

Proving $133|a^{18}-b^{18}$ if $\gcd(a,133)=\gcd(b,133)=1$.

Compute $5^{15}$ mod $7$ using the fact that if gcd$(a,n) = 1$, then $a^{\phi(n)}$ mod $n$ = $1$ (Euler-phi function).

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