Question

How to approach this divisibility problem on polynomial

score 752 · Answer 1 · 2019-05-03 16:40:37

752

Views

How to approach this divisibility problem on polynomial

Published on 03 May 2019 - 16:40

score 78 · Answer 2 · 2026-02-23 04:56:22

78

Views

Two integers $a$ and $b$ are coprime, is it possible that $a \mid b$?

Published on 23 Feb 2026 - 4:56

score 1.6k · Answer 3 · 2026-03-26 20:25:46

1.6k

Views

Factorials and prime numbers

Published on 26 Mar 2026 - 20:25

score 903 · Answer 4 · 2019-05-04 22:08:10

903

Views

Testing divisibility by 7 of number in base 8

Published on 04 May 2019 - 22:08

score 231 · Answer 5 · 2019-05-05 13:40:23

231

Views

Prove $(c^2-1)/4 \pm 1$ is not divisible by $2, 3, $ or $5$ if $c>3$ is an odd prime

Published on 05 May 2019 - 13:40

score 286 · Answer 6 · 2026-03-25 17:21:49

286

Views

Prove $a^t$ is congruent to $1$ modulo one of the primes $p,q$ and $-1$ modulo the other prime.

Published on 25 Mar 2026 - 17:21

score 74 · Answer 7 · 2019-05-08 03:17:28

74

Views

Division of a three-place number into a five-place number, each digit have been replaced by a code letter, reconstruct and show solution is unique.

Published on 08 May 2019 - 3:17

score 42 · Answer 8 · 2019-05-08 23:23:15

42

Views

For all $n\in \mathbb{N}$, find the values for$\big( \sum_{i=1}^{n} (-1)^i i! \big) \mod 36$

Published on 08 May 2019 - 23:23

score 262 · Answer 9 · 2019-05-10 10:08:05

262

Views

Does there exist polynomials $P$ s.t. $P(k)\mid k!$ holds for only finitely many $k\in\Bbb N$?

Published on 10 May 2019 - 10:08

score 50 · Answer 10 · 2019-05-12 15:45:20

50

Views

for each natural number n, the numbers $4^{4n + 2} + 3^{n + 2}$ and $3^{n + 2}$ are coprime.

Published on 12 May 2019 - 15:45

score 102 · Answer 11 · 2019-05-13 01:01:33

102

Views

Prove that for all $n \in \mathbb{N}$, either 3 or 13 divides $3^n + 13n^2 + 38$

Published on 13 May 2019 - 1:01

score 44 · Answer 12 · 2019-05-13 03:51:02

44

Views

Finding the remainder of the division of $\sum_{i=0}^{102} i^6+i$ by 4 and by 5

Published on 13 May 2019 - 3:51

score 104 · Answer 13 · 2019-05-13 06:17:40

104

Views

Congruences and second-order recurrence relations

Published on 13 May 2019 - 6:17

score 113 · Answer 14 · 2019-05-13 11:03:32

113

Views

How can I prove that $3| (4^n - 1)$

Published on 13 May 2019 - 11:03

score 98 · Answer 15 · 2026-02-23 01:23:34

98

Views

Why is it that exponents that are divisors of φ(N) capable of generating the identity element as a power when N is prime?

Published on 23 Feb 2026 - 1:23

List Question

How to approach this divisibility problem on polynomial

Two integers $a$ and $b$ are coprime, is it possible that $a \mid b$?

Factorials and prime numbers

Testing divisibility by 7 of number in base 8

Prove $(c^2-1)/4 \pm 1$ is not divisible by $2, 3, $ or $5$ if $c>3$ is an odd prime

Prove $a^t$ is congruent to $1$ modulo one of the primes $p,q$ and $-1$ modulo the other prime.

Division of a three-place number into a five-place number, each digit have been replaced by a code letter, reconstruct and show solution is unique.

For all $n\in \mathbb{N}$, find the values for$\big( \sum_{i=1}^{n} (-1)^i i! \big) \mod 36$

Does there exist polynomials $P$ s.t. $P(k)\mid k!$ holds for only finitely many $k\in\Bbb N$?

for each natural number n, the numbers $4^{4n + 2} + 3^{n + 2}$ and $3^{n + 2}$ are coprime.

Prove that for all $n \in \mathbb{N}$, either 3 or 13 divides $3^n + 13n^2 + 38$

Finding the remainder of the division of $\sum_{i=0}^{102} i^6+i$ by 4 and by 5

Congruences and second-order recurrence relations

How can I prove that $3| (4^n - 1)$

Why is it that exponents that are divisors of φ(N) capable of generating the identity element as a power when N is prime?

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