Question

Find, with proof, the largest natural number k such that 10^k divides 100! (one hundred factorial).

score 66 · Answer 1 · 2018-11-28 21:51:55

66

Views

Find, with proof, the largest natural number k such that 10^k divides 100! (one hundred factorial).

Published on 28 Nov 2018 - 21:51

score 144 · Answer 2 · 2018-11-29 08:06:42

144

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How to prove: 6 | x(x+1)(x+2)

Published on 29 Nov 2018 - 8:06

score 200 · Answer 3 · 2018-11-29 22:26:18

200

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If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$

Published on 29 Nov 2018 - 22:26

score 223 · Answer 4 · 2018-11-30 02:45:54

223

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$r(n)$ is the sum of the remainders when $n$ is divided by $1,2...,n$ ...

Published on 30 Nov 2018 - 2:45

score 45 · Answer 5 · 2018-12-02 13:20:55

45

Views

Congruence of $29^p \pmod p$

Published on 02 Dec 2018 - 13:20

score 36 · Answer 6 · 2018-12-02 17:19:22

36

Views

simple problem on divides

Published on 02 Dec 2018 - 17:19

score 60 · Answer 7 · 2026-03-23 10:25:38

60

Views

Invertibility as Criteria for a Loop

Published on 23 Mar 2026 - 10:25

score 99 · Answer 8 · 2026-03-26 08:04:40

99

Views

Does $N(mn)|N(m)N(n)$ for $\gcd(m,n)=1$? (Fibonacci Sequence)

Published on 26 Mar 2026 - 8:04

score 107 · Answer 9 · 2018-12-04 22:09:44

107

Views

$3\mid n,m\Rightarrow 3\mid n^2, jn+km\,$ Multiples closed under scalings and addition.

Published on 04 Dec 2018 - 22:09

score 85 · Answer 10 · 2018-12-05 03:12:39

85

Views

Existence of divisor of multiple of primes congruent to 1 mod 4

Published on 05 Dec 2018 - 3:12

score 841 · Answer 11 · 2018-12-05 18:51:30

841

Views

Divisibility Tests in Various Bases

Published on 05 Dec 2018 - 18:51

score 73 · Answer 12 · 2026-03-26 09:58:11

73

Views

If $m, n>0$ and $\gcd(m, n) =d$, then $\gcd(a^m-1, a^n-1) =a^d-1$.

Published on 26 Mar 2026 - 9:58

score 48 · Answer 13 · 2018-12-09 00:55:09

48

Views

Why is $5$ the remainder of $5 \over 13$?

Published on 09 Dec 2018 - 0:55

score 67 · Answer 14 · 2018-12-09 08:40:21

67

Views

For what primes $p \nmid \gcd(a,b,c)$ does $p \mid a+b+c \implies p \nmid a^2+b^2+c^2$?

Published on 09 Dec 2018 - 8:40

score 373 · Answer 15 · 2018-12-10 13:08:57

373

Views

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

Published on 10 Dec 2018 - 13:08

List Question

Find, with proof, the largest natural number k such that 10^k divides 100! (one hundred factorial).

How to prove: 6 | x(x+1)(x+2)

If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$

$r(n)$ is the sum of the remainders when $n$ is divided by $1,2...,n$ ...

Congruence of $29^p \pmod p$

simple problem on divides

Invertibility as Criteria for a Loop

Does $N(mn)|N(m)N(n)$ for $\gcd(m,n)=1$? (Fibonacci Sequence)

$3\mid n,m\Rightarrow 3\mid n^2, jn+km\,$ Multiples closed under scalings and addition.

Existence of divisor of multiple of primes congruent to 1 mod 4

Divisibility Tests in Various Bases

If $m, n>0$ and $\gcd(m, n) =d$, then $\gcd(a^m-1, a^n-1) =a^d-1$.

Why is $5$ the remainder of $5 \over 13$?

For what primes $p \nmid \gcd(a,b,c)$ does $p \mid a+b+c \implies p \nmid a^2+b^2+c^2$?

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

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