Question

Show that $\forall n\in\mathbb{N}$, $\frac{(7n)!}{7^nn!}\equiv(-1)^n\pmod7$

score 59 · Answer 1 · 2026-04-15 16:59:03

59

Views

Show that $\forall n\in\mathbb{N}$, $\frac{(7n)!}{7^nn!}\equiv(-1)^n\pmod7$

Published on 15 Apr 2026 - 16:59

score 40 · Answer 2 · 2026-04-17 06:29:27

40

Views

Find the remainder when 5^23 + 4^6 is divided by 10

Published on 17 Apr 2026 - 6:29

score 424 · Answer 3 · 2026-04-17 13:36:48

424

Views

Chinese Remainder for x= 7 (mod 8), x= 2 (mod 9), x= -1 (mod 5)

Published on 17 Apr 2026 - 13:36

score 244 · Answer 4 · 2026-04-16 13:20:56

244

Views

Prove that $x^2 + y^2 \equiv 3\,mod\,m$ has and integer solution for every m

Published on 16 Apr 2026 - 13:20

score 187 · Answer 5 · 2026-03-25 09:29:22

187

Views

Finding $Z(N)=\sum_{i=1}^N i^2\left\lfloor \frac{N}{i^2} \right\rfloor$

Published on 25 Mar 2026 - 9:29

score 110 · Answer 6 · 2026-03-25 19:07:08

110

Views

Cardinal number of $U(\Bbb Z / 4 \Bbb Z \times \Bbb Z/5 \Bbb Z)$ and zero divisors of $\Bbb Z / 45 \Bbb Z \times \Bbb Z / 27 \Bbb Z$

Published on 25 Mar 2026 - 19:07

score 109 · Answer 7 · 2026-04-15 14:34:34

109

Views

Modulo notation in cryptography

Published on 15 Apr 2026 - 14:34

score 356 · Answer 8 · 2026-04-16 12:46:28

356

Views

Efficient computation of $\sum_{i=1}^{i=\left \lfloor {\sqrt{N}} \right \rfloor}\left \lfloor \frac{N}{i^{2}} \right \rfloor$

Published on 16 Apr 2026 - 12:46

score 37 · Answer 9 · 2026-04-16 19:50:32

37

Views

Congruence arithmetic and a toy NTRU cryptosystem

Published on 16 Apr 2026 - 19:50

score 588 · Answer 10 · 2026-04-22 11:07:47

588

Views

Solving modulus equations with multiple unknowns

Published on 22 Apr 2026 - 11:07

score 306 · Answer 11 · 2026-04-09 13:32:16

306

Views

Coprime group element multiplication

Published on 09 Apr 2026 - 13:32

score 642 · Answer 12 · 2026-04-14 05:10:53

642

Views

System of congruences when $gcd(m,n) \not= 1$

Published on 14 Apr 2026 - 5:10

score 53 · Answer 13 · 2026-04-16 12:23:42

53

Views

What is most efficient way to find the sum of the series: (N/2^2)2^2+(N/3^2)3^2+(N/4^2)*4^2+........

Published on 16 Apr 2026 - 12:23

score 36 · Answer 14 · 2026-04-15 04:39:58

36

Views

Is the residue class of $f(n)$ modulo $n$ always an affine function of the prime factors of $n$?

Published on 15 Apr 2026 - 4:39

score 32 · Answer 15 · 2026-04-14 18:17:28

32

Views

Tips to find the minimum period of an exponential congruence

Published on 14 Apr 2026 - 18:17

List Question

Show that $\forall n\in\mathbb{N}$, $\frac{(7n)!}{7^nn!}\equiv(-1)^n\pmod7$

Find the remainder when 5^23 + 4^6 is divided by 10

Chinese Remainder for x= 7 (mod 8), x= 2 (mod 9), x= -1 (mod 5)

Prove that $x^2 + y^2 \equiv 3\,mod\,m$ has and integer solution for every m

Finding $Z(N)=\sum_{i=1}^N i^2\left\lfloor \frac{N}{i^2} \right\rfloor$

Cardinal number of $U(\Bbb Z / 4 \Bbb Z \times \Bbb Z/5 \Bbb Z)$ and zero divisors of $\Bbb Z / 45 \Bbb Z \times \Bbb Z / 27 \Bbb Z$

Modulo notation in cryptography

Efficient computation of $\sum_{i=1}^{i=\left \lfloor {\sqrt{N}} \right \rfloor}\left \lfloor \frac{N}{i^{2}} \right \rfloor$

Congruence arithmetic and a toy NTRU cryptosystem

Solving modulus equations with multiple unknowns

Coprime group element multiplication

System of congruences when $gcd(m,n) \not= 1$

What is most efficient way to find the sum of the series: (N/2^2)2^2+(N/3^2)3^2+(N/4^2)*4^2+........

Is the residue class of $f(n)$ modulo $n$ always an affine function of the prime factors of $n$?

Tips to find the minimum period of an exponential congruence

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