Question

Prove there exist n that satisfies $S_n = 1! + 2! + .... +n!$ have prime divisor greater than $10^{2020}$.

score 347 · Answer 1 · 2026-03-30 03:05:23

347

Views

Prove there exist n that satisfies $S_n = 1! + 2! + .... +n!$ have prime divisor greater than $10^{2020}$.

Published on 30 Mar 2026 - 3:05

score 207 · Answer 2 · 2020-04-02 17:00:44

207

Views

There is a number, the second digit of which is smaller than its first digit by 4, and if the number

Published on 02 Apr 2020 - 17:00

score 1.4k · Answer 3 · 2020-04-02 17:54:53

1.4k

Views

Count of 6-digit numbers divisible by 6 but not by 9

Published on 02 Apr 2020 - 17:54

score 80 · Answer 4 · 2026-02-23 10:17:35

80

Views

Prove that $\left(A+B\right)^{2}\nmid A^{2n+1}+B^{2n+1}$

Published on 23 Feb 2026 - 10:17

score 37 · Answer 5 · 2026-03-25 20:11:54

37

Views

On integers $n\geq 1$ for which $n$ divides $\sum_{k=1}^n R_k$, where $R_k$ denotes the $k$-th Ramanujan prime

Published on 25 Mar 2026 - 20:11

score 43 · Answer 6 · 2020-04-04 04:22:02

43

Views

relation between concatenation and addition regarding modular arithmetic

Published on 04 Apr 2020 - 4:22

score 1.4k · Answer 7 · 2020-04-04 05:31:54

1.4k

Views

Find all primes $p$, $q$ such that $pq|(5^p - 2^p)(5^q - 2^q)$.

Published on 04 Apr 2020 - 5:31

score 43 · Answer 8 · 2026-03-25 14:26:57

43

Views

On solutions of $\varphi(n)=\frac{1}{2n}\sum_{1\leq d\mid n}\varphi(dn)$, where $\varphi(m)$ denotes the Euler's totient function

Published on 25 Mar 2026 - 14:26

score 413 · Answer 9 · 2026-03-29 04:26:28

413

Views

Proof that if $\gcd(a,p^2)=p$ and $\gcd(b,p^3)=p^2$ then $(ab,p^4)=p^3$

Published on 29 Mar 2026 - 4:26

score 58 · Answer 10 · 2020-04-05 15:57:52

58

Views

Prove that following is always divisble by 5

Published on 05 Apr 2020 - 15:57

score 96 · Answer 11 · 2026-03-26 07:58:34

96

Views

Divisibility of Coefficient Related to Cyclotomic Integer

Published on 26 Mar 2026 - 7:58

score 119 · Answer 12 · 2020-04-05 19:44:11

119

Views

$a,b \in R$ a ring. If $a | b$ in $R$ then $bR\subseteq aR$?

Published on 05 Apr 2020 - 19:44

score 45 · Answer 13 · 2020-04-06 06:45:41

45

Views

Stuck with induction Divisibility

Published on 06 Apr 2020 - 6:45

score 119 · Answer 14 · 2026-03-26 09:48:18

119

Views

Calculating remainder when a polynomial I'd divided by another polynomial

Published on 26 Mar 2026 - 9:48

score 44 · Answer 15 · 2020-04-06 12:05:42

44

Views

Proving a property with the Euclidean division properties

Published on 06 Apr 2020 - 12:05

List Question

Prove there exist n that satisfies $S_n = 1! + 2! + .... +n!$ have prime divisor greater than $10^{2020}$.

There is a number, the second digit of which is smaller than its first digit by 4, and if the number

Count of 6-digit numbers divisible by 6 but not by 9

Prove that $\left(A+B\right)^{2}\nmid A^{2n+1}+B^{2n+1}$

On integers $n\geq 1$ for which $n$ divides $\sum_{k=1}^n R_k$, where $R_k$ denotes the $k$-th Ramanujan prime

relation between concatenation and addition regarding modular arithmetic

Find all primes $p$, $q$ such that $pq|(5^p - 2^p)(5^q - 2^q)$.

On solutions of $\varphi(n)=\frac{1}{2n}\sum_{1\leq d\mid n}\varphi(dn)$, where $\varphi(m)$ denotes the Euler's totient function

Proof that if $\gcd(a,p^2)=p$ and $\gcd(b,p^3)=p^2$ then $(ab,p^4)=p^3$

Prove that following is always divisble by 5

Divisibility of Coefficient Related to Cyclotomic Integer

$a,b \in R$ a ring. If $a | b$ in $R$ then $bR\subseteq aR$?

Stuck with induction Divisibility

Calculating remainder when a polynomial I'd divided by another polynomial

Proving a property with the Euclidean division properties

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