Question

Calculate $27^{162} \pmod {41}$

score 181 · Answer 1 · 2026-04-13 23:19:01

181

Views

Calculate $27^{162} \pmod {41}$

Published on 13 Apr 2026 - 23:19

score 41 · Answer 2 · 2020-02-20 18:08:09

41

Views

Show that if $N = p^c$ for some prime $p$ and $a = p^c + 1 − p^{c−1}$, then $a^{N−1} \not≡ 1 \bmod N$

Published on 20 Feb 2020 - 18:08

score 144 · Answer 3 · 2026-03-28 20:53:10

144

Views

A $p$-congruence involving binomial coefficients and the floor function.

Published on 28 Mar 2026 - 20:53

score 50 · Answer 4 · 2026-04-13 23:34:09

50

Views

What is the probability that the sum of a subset of the remainders a number m excluding 0 of gives you a multiple of m?

Published on 13 Apr 2026 - 23:34

score 76 · Answer 5 · 2026-03-28 03:01:07

76

Views

Am i able to calculate ($a^{bc}$ mod d) with ($a^{b}$ mod d) and ($a^{c}$ mod d) without knowing a power?

Published on 28 Mar 2026 - 3:01

score 121 · Answer 6 · 2026-04-09 13:20:53

121

Views

Modular arithmetic - re-arranging equation to get outcome

Published on 09 Apr 2026 - 13:20

score 543 · Answer 7 · 2026-04-14 13:06:12

543

Views

Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?

Published on 14 Apr 2026 - 13:06

score 755 · Answer 8 · 2026-03-27 13:48:32

755

Views

Let $p$ be an odd prime and let $m = 2p$. Prove that $a^{m−1} ≡ a \pmod{m}$ for all natural numbers $a$.

Published on 27 Mar 2026 - 13:48

score 78 · Answer 9 · 2026-04-14 01:29:02

78

Views

Find the set of integer solutions to the following equation

Published on 14 Apr 2026 - 1:29

score 257 · Answer 10 · 2026-03-25 17:53:13

257

Views

How to compute $\,3^{3^{3^{\:\!\phantom{}^{.^{.^.}}}}}\!\!\!\!\bmod 46,$ for power tower height $2020$?

Published on 25 Mar 2026 - 17:53

score 22 · Answer 11 · 2026-03-21 17:06:52

22

Views

How many equivalence classes have the quotient set of this relation $R$?

Published on 21 Mar 2026 - 17:06

score 1.4k · Answer 12 · 2026-04-12 06:26:49

1.4k

Views

How is calculating the modulus using this formula faster?

Published on 12 Apr 2026 - 6:26

score 106 · Answer 13 · 2026-04-11 05:02:46

106

Views

What is $2007^{2008}\pmod{1000}$?

Published on 11 Apr 2026 - 5:02

score 260 · Answer 14 · 2026-04-12 04:17:29

260

Views

How to calculate $1900^{13} \pmod{2537}$

Published on 12 Apr 2026 - 4:17

score 65 · Answer 15 · 2026-04-13 17:46:31

65

Views

Show $52$ has an inverse in the multiplicative group modulo $109$

Published on 13 Apr 2026 - 17:46

List Question

Calculate $27^{162} \pmod {41}$

Show that if $N = p^c$ for some prime $p$ and $a = p^c + 1 − p^{c−1}$, then $a^{N−1} \not≡ 1 \bmod N$

A $p$-congruence involving binomial coefficients and the floor function.

What is the probability that the sum of a subset of the remainders a number m excluding 0 of gives you a multiple of m?

Am i able to calculate ($a^{bc}$ mod d) with ($a^{b}$ mod d) and ($a^{c}$ mod d) without knowing a power?

Modular arithmetic - re-arranging equation to get outcome

Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?

Let $p$ be an odd prime and let $m = 2p$. Prove that $a^{m−1} ≡ a \pmod{m}$ for all natural numbers $a$.

Find the set of integer solutions to the following equation

How to compute $\,3^{3^{3^{\:\!\phantom{}^{.^{.^.}}}}}\!\!\!\!\bmod 46,$ for power tower height $2020$?

How many equivalence classes have the quotient set of this relation $R$?

How is calculating the modulus using this formula faster?

What is $2007^{2008}\pmod{1000}$?

How to calculate $1900^{13} \pmod{2537}$

Show $52$ has an inverse in the multiplicative group modulo $109$

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