List questions from divisibility

Published on 18 Oct 2018 - 20:44

144

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Let $a\mid bc $ then prove or disprove $a\mid (a,b)c$

Published on 26 Mar 2026 - 3:11

102

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If $\langle g \rangle$ is the only subgroup of order $p$, what's the order of elements $xg$?

Published on 19 Oct 2018 - 20:07

143

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Finite automata {0,...,9} that reads the digits of integer n (left to right) and accepts if n mod 7=1

Published on 21 Oct 2018 - 18:24

178

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Show that $37|333^{777} + 777^{333}$

Published on 22 Oct 2018 - 20:34

4k

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Find the remainder without using long division

Published on 23 Oct 2018 - 17:55

704

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$a^n-a + 1 $ divisible by $n$

Published on 24 Oct 2018 - 8:10

14

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Moving divisions to the opposite side

Published on 03 Mar 2026 - 14:01

211

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Number theory textbook exercise $11^{n+2} + 12^{2n + 1}$

Published on 25 Oct 2018 - 5:52

51

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$\Pi_{i=1}^{p-1}(i-1)kp + i \equiv -1 \pmod p, k \in \mathbb{Z}$ where $p$ is a prime

Published on 25 Oct 2018 - 14:53

188

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div and mod functions over $\Bbb{Z}$

Published on 26 Oct 2018 - 7:49

2.2k

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Divisibility 1,2,3,4,5,6,7,8,9,&10

Published on 25 Mar 2026 - 16:27

76

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Direct proof square

Published on 27 Oct 2018 - 4:22

80

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Divisibility rule

Published on 25 Mar 2026 - 18:04

1.3k

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Prove that infinitely many integers $n$ satisfy $(n+a)\mid(a^n+1)$

Published on 28 Oct 2018 - 8:38

List Question

If a|b and b|c , (how can I prove) ⇒ a|c?

Let $a\mid bc $ then prove or disprove $a\mid (a,b)c$

If $\langle g \rangle$ is the only subgroup of order $p$, what's the order of elements $xg$?

Finite automata {0,...,9} that reads the digits of integer n (left to right) and accepts if n mod 7=1

Show that $37|333^{777} + 777^{333}$

Find the remainder without using long division

$a^n-a + 1 $ divisible by $n$

Moving divisions to the opposite side

Number theory textbook exercise $11^{n+2} + 12^{2n + 1}$

$\Pi_{i=1}^{p-1}(i-1)kp + i \equiv -1 \pmod p, k \in \mathbb{Z}$ where $p$ is a prime

div and mod functions over $\Bbb{Z}$

Divisibility 1,2,3,4,5,6,7,8,9,&10

Direct proof square

Divisibility rule

Prove that infinitely many integers $n$ satisfy $(n+a)\mid(a^n+1)$

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