List questions from divisibility

Published on 15 Jan 2017 - 18:14

52

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Non-trivial solutions of $x(x-1) \equiv 0 \ (\text{mod} \ 10^k)$

Published on 17 Jan 2017 - 0:49

68

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Question about number theory - divisibility by $2^n$ ($n$ is large)

Published on 17 Jan 2017 - 17:16

61

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Divisibility test without using PMI

Published on 18 Jan 2017 - 5:45

101

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Prove $2^{3n}3^n | (4n)!$ Algebraically

Published on 01 Apr 2026 - 5:49

575

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Suppose k and l are relatively prime positive integers. What is gcd($k^2 + l^2$, $k + l$)?

Published on 30 Mar 2026 - 21:43

76

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Prove: If $a^5|b^3$, then $a|b$ for integers $a, b$.

Published on 30 Mar 2026 - 6:45

2.3k

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Show that if $p$ is a prime satisfying $n<p<2n$ then $\binom{2n}{n}\equiv 0 \pmod p$.

Published on 19 Jan 2017 - 2:59

79

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If $a^5|b^3$, does $a^2|b$?

Published on 30 Mar 2026 - 6:48

1.5k

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Why does $987,654,321$ divided by $123,456,789 = 8$?

Published on 29 Mar 2026 - 21:58

39

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Prove if n, i, j are integers with 1$\leq i<j\leq n$ then $\gcd (n!i+1, n!j+1) = 1$

Published on 20 Jan 2017 - 1:56

674

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Let $n>1$ be an odd integer . Show that $n\nmid 3^n+1$

Published on 27 Mar 2026 - 23:00

137

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Alternative Proof of ${{p^\alpha-1}\choose{k}} \equiv ({-1})^k (mod \ p)$

Published on 21 Jan 2017 - 8:38

210

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Find the smallest number that doesn't divide $1 * 2 * 3 * 4 * 5 * 6 * 7 + 11 * 12 * 13 * 14 * 15 * 16 * 17$

Published on 21 Jan 2017 - 12:32

114

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Prove or disprove that $\exists a,b,c\in\mathbb{Z}_+\ \forall n\in\mathbb{Z}_+\ \exists k\in\mathbb{Z}_+\colon\ a^k+b^k+c^k = 0(\mathrm{mod}\ 2^n)$

Published on 31 Mar 2026 - 6:02

List Question

Proving that $19\mid 5^{2n+1}+3^{n+2} \cdot 2^{n-1}$

Non-trivial solutions of $x(x-1) \equiv 0 \ (\text{mod} \ 10^k)$

Question about number theory - divisibility by $2^n$ ($n$ is large)

Divisibility test without using PMI

Prove $2^{3n}3^n | (4n)!$ Algebraically

Suppose k and l are relatively prime positive integers. What is gcd($k^2 + l^2$, $k + l$)?

Prove: If $a^5|b^3$, then $a|b$ for integers $a, b$.

Show that if $p$ is a prime satisfying $n<p<2n$ then $\binom{2n}{n}\equiv 0 \pmod p$.

If $a^5|b^3$, does $a^2|b$?

Why does $987,654,321$ divided by $123,456,789 = 8$?

Prove if n, i, j are integers with 1$\leq i<j\leq n$ then $\gcd (n!i+1, n!j+1) = 1$

Let $n>1$ be an odd integer . Show that $n\nmid 3^n+1$

Alternative Proof of ${{p^\alpha-1}\choose{k}} \equiv ({-1})^k (mod \ p)$

Find the smallest number that doesn't divide $1 * 2 * 3 * 4 * 5 * 6 * 7 + 11 * 12 * 13 * 14 * 15 * 16 * 17$

Prove or disprove that $\exists a,b,c\in\mathbb{Z}_+\ \forall n\in\mathbb{Z}_+\ \exists k\in\mathbb{Z}_+\colon\ a^k+b^k+c^k = 0(\mathrm{mod}\ 2^n)$

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