List questions from congruences

Published on 18 Oct 2017 - 2:10

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Why does this polynomial equation have exactly $q-1$ solutions modulo $p$?

Published on 29 Mar 2026 - 14:18

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Quadratic residue classes

Published on 29 Mar 2026 - 14:27

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Find the number of solutions of $x^{39} ≡ x \pmod {39}$ in the set $\{0, 1 , 2, ..., 38\}$

Published on 31 Mar 2026 - 13:15

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Find all posible $x$ given the congruence $(x+y)^p-y^p \equiv 1 \pmod{q}$ for both $p<q$ prime?

Published on 23 Oct 2017 - 20:56

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Cubic roots modulus prime

Published on 26 Oct 2017 - 22:46

908

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Prove that $n^2 \equiv 1 \ (\mathrm{mod}\ 24)$

Published on 27 Oct 2017 - 16:01

34

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find the value of (a^n!)%p

Published on 28 Oct 2017 - 3:38

1k

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Number of $k$th Roots modulo a prime?

Published on 29 Mar 2026 - 23:43

33

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Prove if $a|3c-b$ and $6c \equiv 4b \pmod a$ then $a|2b$

Published on 30 Oct 2017 - 4:00

604

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Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$

Published on 30 Oct 2017 - 16:06

785

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Prove that $9^{n+1} - 8n- 9$ divisible by $64$

Published on 30 Oct 2017 - 16:33

555

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Numbers $a^{p}a^q$ congruent to 1 modulo pq

Published on 30 Oct 2017 - 17:48

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Sum of positive divisors if and only if perfect square

Published on 30 Mar 2026 - 15:14

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Induction proof: $2^n + 3^n ≡ 5^n (mod 6)$

Published on 31 Oct 2017 - 3:14

List Question

Sum of fifth powers using congruences

Why does this polynomial equation have exactly $q-1$ solutions modulo $p$?

Quadratic residue classes

Find the number of solutions of $x^{39} ≡ x \pmod {39}$ in the set $\{0, 1 , 2, ..., 38\}$

Find all posible $x$ given the congruence $(x+y)^p-y^p \equiv 1 \pmod{q}$ for both $p<q$ prime?

Cubic roots modulus prime

Prove that $n^2 \equiv 1 \ (\mathrm{mod}\ 24)$

find the value of (a^n!)%p

Number of $k$th Roots modulo a prime?

Prove if $a|3c-b$ and $6c \equiv 4b \pmod a$ then $a|2b$

Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$

Prove that $9^{n+1} - 8n- 9$ divisible by $64$

Numbers $a^{p}a^q$ congruent to 1 modulo pq

Sum of positive divisors if and only if perfect square

Induction proof: $2^n + 3^n ≡ 5^n (mod 6)$

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