Question

How many divisors of $\phi(m)$ do not divide $m-1$?

score 136 · Answer 1 · 2019-08-08 12:58:03

136

Views

How many divisors of $\phi(m)$ do not divide $m-1$?

Published on 08 Aug 2019 - 12:58

score 1.7k · Answer 2 · 2019-08-08 15:34:34

1.7k

Views

Proof that if $5\mid2a$, then $5\mid{a}$

Published on 08 Aug 2019 - 15:34

score 97 · Answer 3 · 2019-08-09 07:48:22

If you increase a natural number by the sum of its digits each time from $1$, can you get to $2019\,2019\,2019\,2019$ after a finite number of steps?

score 28 · Answer 4 · 2026-03-25 16:02:16

28

Views

Does $\gcd(r, \sigma(r)) = 2r - \sigma(r)$ always hold when $r$ is deficient-perfect?

Published on 25 Mar 2026 - 16:02

score 2.9k · Answer 5 · 2019-08-11 14:36:37

2.9k

Views

How many positive integers n are there such that $3\le n\le 100$ and $x^{2^n}+x+1$ is divisible by $x^2+x+1$?

Published on 11 Aug 2019 - 14:36

score 467 · Answer 6 · 2019-08-12 07:40:47

467

Views

Show that $n^4-6n^3+11n^2-6n$ is divisible by $4$ for every integer $n$.

Published on 12 Aug 2019 - 7:40

score 96 · Answer 7 · 2019-08-12 13:18:56

96

Views

if $2^n+1=xy$, show $2^a|(x-1) \iff 2^a|(y-1)$

Published on 12 Aug 2019 - 13:18

score 81 · Answer 8 · 2019-08-12 23:30:52

81

Views

For which odd positive integer $n$, is it true that $−1$ is not a positive power of $2$ modulo $n$? [request for more extensive results]

Published on 12 Aug 2019 - 23:30

score 49 · Answer 9 · 2019-08-13 02:09:58

49

Views

How to explain the connection between divisions of a large number?

Published on 13 Aug 2019 - 2:09

score 194 · Answer 10 · 2026-03-27 05:36:24

194

Views

Show that $(a!)^b b! \mid (ab)! $

Published on 27 Mar 2026 - 5:36

score 34 · Answer 11 · 2019-08-13 11:17:20

34

Views

Does $x$ include $1$ and $y$ when we say $x\mid y$?

Published on 13 Aug 2019 - 11:17

score 157 · Answer 12 · 2026-03-25 11:27:19

157

Views

Find all ordered triples of primes $(a, b, c)$ such that $a \mid {^bc} + 1, b \mid {^ca} + 1, c \mid {^ab} + 1$.

Published on 25 Mar 2026 - 11:27

score 56 · Answer 13 · 2019-08-15 07:22:22

If the number of distinct five-digits $1A54B$ is divided by $24$ , then the remainder is 15, what is the sum of the different values A can take?

score 124 · Answer 14 · 2026-03-27 05:41:56

124

Views

What is longer? Length of $2^n$ or number of $0$ in $n!$?

Published on 27 Mar 2026 - 5:41

score 53 · Answer 15 · 2019-08-15 15:55:22

53

Views

How Can We Infer Non-Existence of Solution from a Congruence?

Published on 15 Aug 2019 - 15:55

List Question

How many divisors of $\phi(m)$ do not divide $m-1$?

Proof that if $5\mid2a$, then $5\mid{a}$

If you increase a natural number by the sum of its digits each time from $1$, can you get to $2019\,2019\,2019\,2019$ after a finite number of steps?

Does $\gcd(r, \sigma(r)) = 2r - \sigma(r)$ always hold when $r$ is deficient-perfect?

How many positive integers n are there such that $3\le n\le 100$ and $x^{2^n}+x+1$ is divisible by $x^2+x+1$?

Show that $n^4-6n^3+11n^2-6n$ is divisible by $4$ for every integer $n$.

if $2^n+1=xy$, show $2^a|(x-1) \iff 2^a|(y-1)$

For which odd positive integer $n$, is it true that $−1$ is not a positive power of $2$ modulo $n$? [request for more extensive results]

How to explain the connection between divisions of a large number?

Show that $(a!)^b b! \mid (ab)! $

Does $x$ include $1$ and $y$ when we say $x\mid y$?

Find all ordered triples of primes $(a, b, c)$ such that $a \mid {^bc} + 1, b \mid {^ca} + 1, c \mid {^ab} + 1$.

If the number of distinct five-digits $1A54B$ is divided by $24$ , then the remainder is 15, what is the sum of the different values A can take?

What is longer? Length of $2^n$ or number of $0$ in $n!$?

How Can We Infer Non-Existence of Solution from a Congruence?

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