List questions from divisibility

Published on 21 Nov 2018 - 19:54

30

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Prove the divisibility of $R^k_n\pm 1$ by 4

Published on 22 Nov 2018 - 12:57

98

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Prove that $\frac{n}{3}+\frac{n^2}{3}+\frac{n^3}{6}$ is natural number

Published on 22 Nov 2018 - 21:24

427

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If $a$ is of order $3$ mod a prime $p$, then ...

Published on 25 Mar 2026 - 11:54

64

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Prove that $1982\cdot 1983|\underbrace{22 \ldots2}_{1980}$

Published on 23 Nov 2018 - 6:57

55

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Meaning of the expression $p^\alpha \mid \mid n$

Published on 23 Nov 2018 - 7:19

856

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Solve equations $x^2+x+1\equiv 0(\mod 7)$ and $2x-4\equiv 0(\mod 6)$

Published on 23 Nov 2018 - 8:24

895

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Show that if $p|(a^{2^n}+1)$, then $p = 2$ or $p\equiv 1 \pmod{2^{n+1}}$

Published on 25 Mar 2026 - 10:35

709

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Find all prime number $p$ such that $2^p+p^2$ is prime number

Published on 23 Nov 2018 - 12:08

492

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Find all number $n\in \mathbb N$ such that $\varphi (n)=14$

Published on 25 Mar 2026 - 23:38

268

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Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1

Published on 23 Nov 2018 - 17:48

830

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When g and -g are both primitive roots

Published on 25 Mar 2026 - 11:53

219

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Show $11^{11}+12^{12}+13^{13} =10k$ without direct calculation

Published on 25 Nov 2018 - 18:46

55

Views

Divisibility of a number by $3$

Published on 26 Nov 2018 - 22:46

26

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if $n = a_1a_2 \cdots a_r + 2$, then $a_i \nmid n$ for each integer $i (1 \leq i \leq r)$.

Published on 28 Nov 2018 - 6:11

List Question

Solve congruence $x^2+x+9\equiv 0 \pmod{63}$

Prove the divisibility of $R^k_n\pm 1$ by 4

Prove that $\frac{n}{3}+\frac{n^2}{3}+\frac{n^3}{6}$ is natural number

If $a$ is of order $3$ mod a prime $p$, then ...

Prove that $1982\cdot 1983|\underbrace{22 \ldots2}_{1980}$

Meaning of the expression $p^\alpha \mid \mid n$

Solve equations $x^2+x+1\equiv 0(\mod 7)$ and $2x-4\equiv 0(\mod 6)$

Show that if $p|(a^{2^n}+1)$, then $p = 2$ or $p\equiv 1 \pmod{2^{n+1}}$

Find all prime number $p$ such that $2^p+p^2$ is prime number

Find all number $n\in \mathbb N$ such that $\varphi (n)=14$

Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1

When g and -g are both primitive roots

Show $11^{11}+12^{12}+13^{13} =10k$ without direct calculation

Divisibility of a number by $3$

if $n = a_1a_2 \cdots a_r + 2$, then $a_i \nmid n$ for each integer $i (1 \leq i \leq r)$.

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