Question

Prove that if $p \mid a-b$ then $p^{n+1} \mid a^{p^n}-b^{p^n}$

score 153 · Answer 1 · 2026-04-16 22:43:15

153

Views

Prove that if $p \mid a-b$ then $p^{n+1} \mid a^{p^n}-b^{p^n}$

Published on 16 Apr 2026 - 22:43

score 247 · Answer 2 · 2026-04-12 08:28:55

247

Views

Divisibility - what is A+B?

Published on 12 Apr 2026 - 8:28

score 101 · Answer 3 · 2026-04-16 05:12:08

101

Views

Show there are only a finite number of integers with $\dfrac{\prod_{i=1}^n a_i-1}{\prod_{i=1}^n (a_i-1)} $ an integer

Published on 16 Apr 2026 - 5:12

score 4.4k · Answer 4 · 2026-04-10 12:04:30

4.4k

Views

Proving that an equation doesn't have integer solutions

Published on 10 Apr 2026 - 12:04

score 92 · Answer 5 · 2026-04-17 08:36:27

92

Views

If $9 \mid 2^b-2^a$, then $7\mid2^b-2^a$

Published on 17 Apr 2026 - 8:36

score 2k · Answer 6 · 2026-04-09 11:16:32

2k

Views

Dividing by something Undefined

Published on 09 Apr 2026 - 11:16

score 2.1k · Answer 7 · 2026-04-13 18:52:22

2.1k

Views

How to find remainder of a very large number when divisor is 17?

Published on 13 Apr 2026 - 18:52

score 249 · Answer 8 · 2026-04-17 16:49:35

249

Views

Given that an expression $2x^3+px^2-8x+q$ is exactly divisible by $2x^2-7x+6$, determine the value of $p$ and $q$.

Published on 17 Apr 2026 - 16:49

score 21 · Answer 9 · 2026-04-09 03:53:37

21

Views

Need help in understanding a solution regarding divisibility

Published on 09 Apr 2026 - 3:53

score 975 · Answer 10 · 2026-04-11 19:34:08

975

Views

Lattices and Boolean algebra

Published on 11 Apr 2026 - 19:34

score 231 · Answer 11 · 2026-03-29 23:58:48

231

Views

A very difficult Diophantine problem $n^2 \mid 3^n+2^n+1$

Published on 29 Mar 2026 - 23:58

score 2k · Answer 12 · 2026-04-15 02:59:38

2k

Views

How many $3$ digit different number that will be divisible by $5$ can be formed from the digit $0,2,3,4,5,6$ lying between $100$ and $1000$.

Published on 15 Apr 2026 - 2:59

score 64 · Answer 13 · 2026-04-15 18:51:01

64

Views

Find $b \in \Bbb Z$ for which exists $a \equiv 4 \pmod 5$ such that $6a+21b=15$

Published on 15 Apr 2026 - 18:51

score 57 · Answer 14 · 2026-03-29 22:33:17

57

Views

If $\gcd(a,x)=1$ and $a|x^n-1$, then $n|\varphi(a)$?

Published on 29 Mar 2026 - 22:33

score 667 · Answer 15 · 2026-04-16 14:24:45

667

Views

Find all odd $n \in \mathbb{Z}^+$ such that $n\mid 3^n+1$.

Published on 16 Apr 2026 - 14:24

List Question

Prove that if $p \mid a-b$ then $p^{n+1} \mid a^{p^n}-b^{p^n}$

Divisibility - what is A+B?

Show there are only a finite number of integers with $\dfrac{\prod_{i=1}^n a_i-1}{\prod_{i=1}^n (a_i-1)} $ an integer

Proving that an equation doesn't have integer solutions

If $9 \mid 2^b-2^a$, then $7\mid2^b-2^a$

Dividing by something Undefined

How to find remainder of a very large number when divisor is 17?

Given that an expression $2x^3+px^2-8x+q$ is exactly divisible by $2x^2-7x+6$, determine the value of $p$ and $q$.

Need help in understanding a solution regarding divisibility

Lattices and Boolean algebra

A very difficult Diophantine problem $n^2 \mid 3^n+2^n+1$

How many $3$ digit different number that will be divisible by $5$ can be formed from the digit $0,2,3,4,5,6$ lying between $100$ and $1000$.

Find $b \in \Bbb Z$ for which exists $a \equiv 4 \pmod 5$ such that $6a+21b=15$

If $\gcd(a,x)=1$ and $a|x^n-1$, then $n|\varphi(a)$?

Find all odd $n \in \mathbb{Z}^+$ such that $n\mid 3^n+1$.

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