Question

If $\frac{a^n-1}{b^n-1} $ is a natural number for every $n$ then $a = b^m$

score 125 · Answer 1 · 2016-09-08 18:44:57

125

Views

If $\frac{a^n-1}{b^n-1} $ is a natural number for every $n$ then $a = b^m$

Published on 08 Sep 2016 - 18:44

score 642 · Answer 2 · 2016-09-09 10:34:45

642

Views

Proof using induction: $r!$ divides the product of $r$ consecutive integers

Published on 09 Sep 2016 - 10:34

score 63 · Answer 3 · 2016-09-09 17:22:45

63

Views

Find $x$ given remainder conditions

Published on 09 Sep 2016 - 17:22

score 238 · Answer 4 · 2016-09-10 13:22:29

238

Views

Prove that the expression is divisible by 247 for any natural number

Published on 10 Sep 2016 - 13:22

score 25k · Answer 5 · 2016-09-10 21:27:27

25k

Views

Prove that if $p$ is a prime, $a$ is an integer, and $p$ divides $a^2$, then $p$ divides $a$.

Published on 10 Sep 2016 - 21:27

score 274 · Answer 6 · 2016-09-11 19:06:52

274

Views

integer with all digits, multiple of 126

Published on 11 Sep 2016 - 19:06

score 922 · Answer 7 · 2016-09-12 01:58:03

Let $a$ and $b$ be integers. We say that $a$ is divisible by $b$ provided there is an integer $c$ such that $bc = a$. Find integers $a$ and $b$.

score 115 · Answer 8 · 2016-09-12 08:50:41

115

Views

Number of $75\leq n\leq 300$ not divisible by any of $9,12,15$ - check work

Published on 12 Sep 2016 - 8:50

score 53 · Answer 9 · 2016-09-12 15:10:31

53

Views

Find all integers $x$ that can't be written as $x=a+b+c$, where $a$ divides $b$ and $b$ divides $c$ with $a<b<c$

Published on 12 Sep 2016 - 15:10

score 465 · Answer 10 · 2026-03-30 02:06:31

465

Views

Show that if a|c, b|c and gcd(a,b)=1, then ab|c

Published on 30 Mar 2026 - 2:06

score 226 · Answer 11 · 2016-09-13 21:53:11

226

Views

Given $p$ prime and $0<k<p$, show that $p$ divides ${p \choose k}$

Published on 13 Sep 2016 - 21:53

score 131 · Answer 12 · 2016-09-16 14:07:48

131

Views

Fibonacci Numbers, Necklaces, Number Theory (modulo 10)

Published on 16 Sep 2016 - 14:07

score 36 · Answer 13 · 2016-09-16 16:54:29

36

Views

For $p$ an odd prime and $i\ge 1$ integer there exists $\nu \in \mathbb{Z}$ such that : $(1+p)^{{p}^{i}}=1+\nu p^{i+1}$

Published on 16 Sep 2016 - 16:54

score 115 · Answer 14 · 2016-09-16 20:39:38

115

Views

$p^n\mid ((p^{n-m}+1)^j-1)$?

Published on 16 Sep 2016 - 20:39

score 38 · Answer 15 · 2026-03-30 02:10:07

38

Views

Problem regarding divisibility and GCD

Published on 30 Mar 2026 - 2:10

List Question

If $\frac{a^n-1}{b^n-1} $ is a natural number for every $n$ then $a = b^m$

Proof using induction: $r!$ divides the product of $r$ consecutive integers

Find $x$ given remainder conditions

Prove that the expression is divisible by 247 for any natural number

Prove that if $p$ is a prime, $a$ is an integer, and $p$ divides $a^2$, then $p$ divides $a$.

integer with all digits, multiple of 126

Let $a$ and $b$ be integers. We say that $a$ is divisible by $b$ provided there is an integer $c$ such that $bc = a$. Find integers $a$ and $b$.

Number of $75\leq n\leq 300$ not divisible by any of $9,12,15$ - check work

Find all integers $x$ that can't be written as $x=a+b+c$, where $a$ divides $b$ and $b$ divides $c$ with $a<b<c$

Show that if a|c, b|c and gcd(a,b)=1, then ab|c

Given $p$ prime and $0<k<p$, show that $p$ divides ${p \choose k}$

Fibonacci Numbers, Necklaces, Number Theory (modulo 10)

For $p$ an odd prime and $i\ge 1$ integer there exists $\nu \in \mathbb{Z}$ such that : $(1+p)^{{p}^{i}}=1+\nu p^{i+1}$

$p^n\mid ((p^{n-m}+1)^j-1)$?

Problem regarding divisibility and GCD

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