Question

Prove that $n \in \mathbb{Z}^\star \Leftrightarrow n \mid 1$ and $n-1 \mid 1$ or $n+1 \mid 1$, and $(x-1)/(t-1) \equiv n \pmod {t-1}$

score 191 · Answer 1 · 2015-07-27 02:56:40

191

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Prove that $n \in \mathbb{Z}^\star \Leftrightarrow n \mid 1$ and $n-1 \mid 1$ or $n+1 \mid 1$, and $(x-1)/(t-1) \equiv n \pmod {t-1}$

Published on 27 Jul 2015 - 2:56

score 62 · Answer 2 · 2026-04-11 07:24:16

62

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Explain 'expressing a number using its digits'

Published on 11 Apr 2026 - 7:24

score 245 · Answer 3 · 2015-07-29 07:34:20

245

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Is $a=\frac{1992!-1}{3449\times 8627}$ a prime number?

Published on 29 Jul 2015 - 7:34

score 1.4k · Answer 4 · 2015-08-01 10:46:39

1.4k

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Dividing the whole into a minimal amount of parts to equally distribute it between different groups.

Published on 01 Aug 2015 - 10:46

score 2.6k · Answer 5 · 2026-04-11 20:15:53

2.6k

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Probability of getting a five digit number divisible by 5 but with no two consecutive digits identical

Published on 11 Apr 2026 - 20:15

score 553 · Answer 6 · 2026-04-10 16:22:41

553

Views

Show divisibility by 7

Published on 10 Apr 2026 - 16:22

score 152 · Answer 7 · 2026-04-09 21:07:38

152

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Division problems

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score 975 · Answer 8 · 2026-04-11 21:41:15

975

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Alternate ways to prove that $4$ divides $5^n-1$

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score 72 · Answer 9 · 2026-04-03 02:39:53

72

Views

If $c = \gcd(a, b)$ then $c^2\mid ab$

Published on 03 Apr 2026 - 2:39

score 280 · Answer 10 · 2015-08-06 01:12:52

280

Views

Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$

Published on 06 Aug 2015 - 1:12

score 123 · Answer 11 · 2015-08-06 06:09:43

123

Views

I have plugged $p/q$ into the equation. Not sure what to do next.

Published on 06 Aug 2015 - 6:09

score 2.5k · Answer 12 · 2015-08-06 22:31:13

2.5k

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Prove that $2730$ divides $n^{13} - n$ for all integers $n$.

Published on 06 Aug 2015 - 22:31

score 820 · Answer 13 · 2026-04-12 05:49:13

820

Views

complex long division

Published on 12 Apr 2026 - 5:49

score 34k · Answer 14 · 2026-04-03 02:42:18

34k

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Prove $\gcd(n, n + 1) = 1$ for any $n$

Published on 03 Apr 2026 - 2:42

score 3.6k · Answer 15 · 2026-04-12 08:09:55

3.6k

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How can I find The Multiplicative Inverse of $1+\sqrt{2}$?

Published on 12 Apr 2026 - 8:09

List Question

Prove that $n \in \mathbb{Z}^\star \Leftrightarrow n \mid 1$ and $n-1 \mid 1$ or $n+1 \mid 1$, and $(x-1)/(t-1) \equiv n \pmod {t-1}$

Explain 'expressing a number using its digits'

Is $a=\frac{1992!-1}{3449\times 8627}$ a prime number?

Dividing the whole into a minimal amount of parts to equally distribute it between different groups.

Probability of getting a five digit number divisible by 5 but with no two consecutive digits identical

Show divisibility by 7

Division problems

Alternate ways to prove that $4$ divides $5^n-1$

If $c = \gcd(a, b)$ then $c^2\mid ab$

Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$

I have plugged $p/q$ into the equation. Not sure what to do next.

Prove that $2730$ divides $n^{13} - n$ for all integers $n$.

complex long division

Prove $\gcd(n, n + 1) = 1$ for any $n$

How can I find The Multiplicative Inverse of $1+\sqrt{2}$?

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