Question

Form of odd primes with totients co-prime to $5$?

score 177 · Answer 1 · 2026-03-26 19:19:05

177

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Form of odd primes with totients co-prime to $5$?

Published on 26 Mar 2026 - 19:19

score 97 · Answer 2 · 2026-03-30 06:44:37

97

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How can we calculate the maximum possible gap?

Published on 30 Mar 2026 - 6:44

score 1.4k · Answer 3 · 2017-01-04 00:56:36

1.4k

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Prove $10^{10^{10^n}} + 10^{10^n} + 10^{n} - 1$ is never prime

Published on 04 Jan 2017 - 0:56

score 66 · Answer 4 · 2026-03-31 19:17:53

66

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Find all pairs of positive integers $(m, n)$ such that $\sum_\limits{k=0}^{m} x^k \mid \sum_\limits{k=0}^{m} x^{kn}$

Published on 31 Mar 2026 - 19:17

score 87 · Answer 5 · 2017-01-05 05:12:18

87

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Find all $n$ such that $n \mid x_n$ where $x_n = x_{n-1} + \lfloor n^2 / 4 \rfloor$, $x_0 = 0$

Published on 05 Jan 2017 - 5:12

score 176 · Answer 6 · 2017-01-05 09:28:25

176

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Divisibility of $(4^{2^{2n+1}}-3)$ by 13.

Published on 05 Jan 2017 - 9:28

score 421 · Answer 7 · 2017-01-05 21:43:31

421

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Polynomials - Relation of Divisibility

Published on 05 Jan 2017 - 21:43

score 115 · Answer 8 · 2017-01-05 22:45:06

115

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Divisibility remainders for $9, 25, 49,$ and $105$.

Published on 05 Jan 2017 - 22:45

score 39 · Answer 9 · 2026-03-31 19:15:04

39

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$\frac{a^{n \tiny\frac{n-2}{2}} - 1}{(n-1)(n+1)} \in \Bbb{Z}$ infinitely often.

Published on 31 Mar 2026 - 19:15

score 338 · Answer 10 · 2017-01-06 12:15:02

338

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Prove that $n-1$ divides $n!\left(1+\sum\limits_{k=2}^{n}\frac{(-1)^k}{k!}\right)$

Published on 06 Jan 2017 - 12:15

score 681 · Answer 11 · 2017-01-07 05:37:48

681

Views

Why there is no operation of matrix division?

Published on 07 Jan 2017 - 5:37

score 238 · Answer 12 · 2017-01-07 12:33:31

238

Views

To Show that $6$ divides $n$ if $6$ $|$ $(p_1 ^2 + p_2 ^2 + p_3 ^2 ......... p_n ^2)$ where $p_i$ is a prime$

Published on 07 Jan 2017 - 12:33

score 80 · Answer 13 · 2017-01-07 19:12:48

80

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Prove that for integers $a,b$, if $3|ab$ with $15x+by = 1$ for some integers $x,y$ then $3|a.$

Published on 07 Jan 2017 - 19:12

score 205 · Answer 14 · 2017-01-08 11:02:05

205

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If $x\ast y = y\ast x$ and $\gcd(o(x),o(y)) = 1$ then $o(xy) = o(x)o(y)$

Published on 08 Jan 2017 - 11:02

score 69 · Answer 15 · 2017-01-08 11:09:54

69

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Find all $n \in \mathbb{N}$ for which $(2^n + n) | (8^n + n)$.

Published on 08 Jan 2017 - 11:09

List Question

Form of odd primes with totients co-prime to $5$?

How can we calculate the maximum possible gap?

Prove $10^{10^{10^n}} + 10^{10^n} + 10^{n} - 1$ is never prime

Find all pairs of positive integers $(m, n)$ such that $\sum_\limits{k=0}^{m} x^k \mid \sum_\limits{k=0}^{m} x^{kn}$

Find all $n$ such that $n \mid x_n$ where $x_n = x_{n-1} + \lfloor n^2 / 4 \rfloor$, $x_0 = 0$

Divisibility of $(4^{2^{2n+1}}-3)$ by 13.

Polynomials - Relation of Divisibility

Divisibility remainders for $9, 25, 49,$ and $105$.

$\frac{a^{n \tiny\frac{n-2}{2}} - 1}{(n-1)(n+1)} \in \Bbb{Z}$ infinitely often.

Prove that $n-1$ divides $n!\left(1+\sum\limits_{k=2}^{n}\frac{(-1)^k}{k!}\right)$

Why there is no operation of matrix division?

To Show that $6$ divides $n$ if $6$ $|$ $(p_1 ^2 + p_2 ^2 + p_3 ^2 ......... p_n ^2)$ where $p_i$ is a prime$

Prove that for integers $a,b$, if $3|ab$ with $15x+by = 1$ for some integers $x,y$ then $3|a.$

If $x\ast y = y\ast x$ and $\gcd(o(x),o(y)) = 1$ then $o(xy) = o(x)o(y)$

Find all $n \in \mathbb{N}$ for which $(2^n + n) | (8^n + n)$.

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