Question

Prove that $13^n -4^n$ is divisible by $9$ for every integer $\geq $

score 2k · Answer 1 · 2016-11-05 06:55:31

2k

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Prove that $13^n -4^n$ is divisible by $9$ for every integer $\geq $

Published on 05 Nov 2016 - 6:55

score 5.5k · Answer 2 · 2026-04-02 20:17:10

5.5k

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Which elements in $\mathbb{Z}_5$ have multiplicative inverses?

Published on 02 Apr 2026 - 20:17

score 147 · Answer 3 · 2016-11-05 18:39:17

147

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Help disproving the following statement.

Published on 05 Nov 2016 - 18:39

score 464 · Answer 4 · 2016-11-06 00:14:59

464

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Please verify my induction proof: $3$| $(5 \cdot 10^{n+1} + 3\cdot 10^n + 4)$ for $n ∈ \mathbb N $

Published on 06 Nov 2016 - 0:14

score 3k · Answer 5 · 2026-03-30 12:45:26

3k

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If gcd(a,c)=1 and b|c, then gcd(a,b)=1?

Published on 30 Mar 2026 - 12:45

score 58 · Answer 6 · 2016-11-07 03:37:10

58

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Show that one combination exists (in $^{11}C_6$, 1 to 11 integers) such that $a^2+b^2+c^2 = d^2+e^2+f^2$ is divisible by 12

Published on 07 Nov 2016 - 3:37

score 51 · Answer 7 · 2016-11-07 17:27:41

51

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We have an ISBN: $\left(\sum_{k=1}^{9}(11-k) \cdot x_{k}+p\right) \text{ mod } 11=0$

Published on 07 Nov 2016 - 17:27

score 80 · Answer 8 · 2016-11-08 12:29:50

80

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Prove that we can always find a and b in S, a not equal to b, such that a divides b.

Published on 08 Nov 2016 - 12:29

score 235 · Answer 9 · 2026-04-03 17:32:39

235

Views

Prove $27195^8 - 10887^8 + 10152^8\equiv 0\pmod{26460}$

Published on 03 Apr 2026 - 17:32

score 61 · Answer 10 · 2026-03-31 07:50:37

61

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Finding 9-digit Positive Integers with Specific Decimal Digits that are Divisible by a Specific number

Published on 31 Mar 2026 - 7:50

score 1.7k · Answer 11 · 2016-11-10 05:48:30

1.7k

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If a prime divides a product then it must divide a factor of the product [Euclid's Lemma]

Published on 10 Nov 2016 - 5:48

score 37 · Answer 12 · 2016-11-10 08:48:07

37

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Is $30$ a factor of $n$?

Published on 10 Nov 2016 - 8:48

score 2.8k · Answer 13 · 2026-04-02 20:07:22

2.8k

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Which elements in $\mathbb{Z}_{12}$ have multiplicative inverses?

Published on 02 Apr 2026 - 20:07

score 3k · Answer 14 · 2016-11-11 16:12:05

3k

Views

Find all solutions; $17x \equiv 25 (\text{ mod } 33)$

Published on 11 Nov 2016 - 16:12

score 108 · Answer 15 · 2016-11-12 00:54:32

108

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Elementary number theory( divisor)

Published on 12 Nov 2016 - 0:54

List Question

Prove that $13^n -4^n$ is divisible by $9$ for every integer $\geq $

Which elements in $\mathbb{Z}_5$ have multiplicative inverses?

Help disproving the following statement.

Please verify my induction proof: $3$| $(5 \cdot 10^{n+1} + 3\cdot 10^n + 4)$ for $n ∈ \mathbb N $

If gcd(a,c)=1 and b|c, then gcd(a,b)=1?

Show that one combination exists (in $^{11}C_6$, 1 to 11 integers) such that $a^2+b^2+c^2 = d^2+e^2+f^2$ is divisible by 12

We have an ISBN: $\left(\sum_{k=1}^{9}(11-k) \cdot x_{k}+p\right) \text{ mod } 11=0$

Prove that we can always find a and b in S, a not equal to b, such that a divides b.

Prove $27195^8 - 10887^8 + 10152^8\equiv 0\pmod{26460}$

Finding 9-digit Positive Integers with Specific Decimal Digits that are Divisible by a Specific number

If a prime divides a product then it must divide a factor of the product [Euclid's Lemma]

Is $30$ a factor of $n$?

Which elements in $\mathbb{Z}_{12}$ have multiplicative inverses?

Find all solutions; $17x \equiv 25 (\text{ mod } 33)$

Elementary number theory( divisor)

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