Question

If $m | (8n +7)$, $m | (6n + 5)$, prove that $m = ± 1$

score 896 · Answer 1 · 2016-02-06 23:25:00

896

Views

If $m | (8n +7)$, $m | (6n + 5)$, prove that $m = ± 1$

Published on 06 Feb 2016 - 23:25

score 747 · Answer 2 · 2026-04-14 23:53:21

747

Views

Remainder when ${45^{17}}^{17}$ is divided by 204

Published on 14 Apr 2026 - 23:53

score 202 · Answer 3 · 2026-04-01 17:06:00

202

Views

Find all $n$ such that $3^{2n+1}-4^{n+1}+6^n$ is prime

Published on 01 Apr 2026 - 17:06

score 7.6k · Answer 4 · 2016-02-10 02:53:51

7.6k

Views

Number of ways of selecting 3 numbers from $\{1,2,3,\cdots,3n\}$ such that the sum is divisible by 3

Published on 10 Feb 2016 - 2:53

score 1.6k · Answer 5 · 2026-04-13 02:37:26

1.6k

Views

What is the sum of all the natural numbers between $500$ and $1000$.

Published on 13 Apr 2026 - 2:37

score 110 · Answer 6 · 2026-04-01 17:07:13

110

Views

Compute a natural number $n\geq 2$ s.t. $p\mid n \Longrightarrow p^2\nmid n$ AND $p-1\mid n \Longleftrightarrow p\mid n$ for all prime divisor p of n.

Published on 01 Apr 2026 - 17:07

score 50 · Answer 7 · 2016-02-12 02:54:48

50

Views

How to work out the greatest lower divisor in a pair of divisors?

Published on 12 Feb 2016 - 2:54

score 129 · Answer 8 · 2026-03-28 06:08:22

129

Views

Determine all $k$ such that $k^3+k+1$ is divisible by 11

Published on 28 Mar 2026 - 6:08

score 102 · Answer 9 · 2016-02-12 15:48:37

102

Views

Prove or reject: if $a^2|b^3$ then $a|b$

Published on 12 Feb 2016 - 15:48

score 109 · Answer 10 · 2026-04-12 05:12:48

109

Views

Prime factorization and hcf

Published on 12 Apr 2026 - 5:12

score 7.4k · Answer 11 · 2016-02-13 18:49:49

7.4k

Views

Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$

Published on 13 Feb 2016 - 18:49

score 47 · Answer 12 · 2026-04-13 17:05:27

47

Views

$a =\prod_{i = 1}^{r} p_{i}^{ai}$ with $a_{i} > 0$ for each $i$ is the canonical representation of $a$...

Published on 13 Apr 2026 - 17:05

score 28 · Answer 13 · 2026-04-01 06:32:18

28

Views

$a =\prod_{i = 1}^{r} p_{i}^{a_i}$ with $a_{i} > 0$ for each $i$ is the canonical representation of $a$...

Published on 01 Apr 2026 - 6:32

score 5k · Answer 14 · 2026-04-11 16:41:36

5k

Views

Counting 3-digit integers divisible by 6 but not by 9

Published on 11 Apr 2026 - 16:41

score 4.8k · Answer 15 · 2026-04-14 13:18:28

4.8k

Views

How to prove $5^n − 1$ is divisible by 4, for each integer n ≥ 0 by mathematical induction?

Published on 14 Apr 2026 - 13:18

List Question

If $m | (8n +7)$, $m | (6n + 5)$, prove that $m = ± 1$

Remainder when ${45^{17}}^{17}$ is divided by 204

Find all $n$ such that $3^{2n+1}-4^{n+1}+6^n$ is prime

Number of ways of selecting 3 numbers from $\{1,2,3,\cdots,3n\}$ such that the sum is divisible by 3

What is the sum of all the natural numbers between $500$ and $1000$.

Compute a natural number $n\geq 2$ s.t. $p\mid n \Longrightarrow p^2\nmid n$ AND $p-1\mid n \Longleftrightarrow p\mid n$ for all prime divisor p of n.

How to work out the greatest lower divisor in a pair of divisors?

Determine all $k$ such that $k^3+k+1$ is divisible by 11

Prove or reject: if $a^2|b^3$ then $a|b$

Prime factorization and hcf

Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$

$a =\prod_{i = 1}^{r} p_{i}^{ai}$ with $a_{i} > 0$ for each $i$ is the canonical representation of $a$...

$a =\prod_{i = 1}^{r} p_{i}^{a_i}$ with $a_{i} > 0$ for each $i$ is the canonical representation of $a$...

Counting 3-digit integers divisible by 6 but not by 9

How to prove $5^n − 1$ is divisible by 4, for each integer n ≥ 0 by mathematical induction?

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