List questions from modular-arithmetic

Published on 03 Feb 2019 - 5:11

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Using Fermat's little theorem to find Multiplicative Inverse

Published on 27 Mar 2026 - 5:58

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Can modulize a multiplication of some numbers

Published on 25 Mar 2026 - 6:05

89

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Prove that $x+x^{3}+x^{5}+x^{7}+x^{9}+x^{11}\equiv 1\mod{11}$ has no solution

Published on 03 Feb 2019 - 20:21

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If $\phi(d)|\phi(n)$ then $d|n$

Published on 04 Feb 2019 - 2:39

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if $d|n$ then $\phi(dn)=d\phi(n)$

Published on 04 Feb 2019 - 4:23

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Show that for any prime $p$ and any integer $m$, $m^p + (p − 1)! m$ is divisible by $p$.

Published on 04 Feb 2019 - 6:04

323

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Show that $1000000! \equiv 500001 \mod 1000003$

Published on 04 Feb 2019 - 6:39

78

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Showing that $-1\not\equiv 5^{n}\pmod{2^k}$.

Published on 04 Feb 2019 - 10:43

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show that the remainder of $\frac{2^{100}}{23}$ is $2$

Published on 04 Feb 2019 - 14:26

109

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for all $n \in {N} : a^n + n | b^n +n$

Published on 28 Mar 2026 - 11:33

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Show that each number of $100!+1,100!+2,100!+3,...,100!+100$ is composite

Published on 04 Feb 2019 - 18:00

135

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Minimize $152207x-81103y$ over the positive integers.

Published on 25 Mar 2026 - 6:10

514

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How can I solve this problem : $2^{x} \equiv{2070442609 \cdots 226509} \pmod {6561}$

Published on 23 Feb 2026 - 2:56

119

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Show that: $-1 \equiv (-1)^{(p-1)/2}x^2 \pmod p$

Published on 05 Feb 2019 - 4:34

List Question

Let $n$ be a positive integer. Show that $n\phi(n)=\phi(n^2).$

Using Fermat's little theorem to find Multiplicative Inverse

Can modulize a multiplication of some numbers

Prove that $x+x^{3}+x^{5}+x^{7}+x^{9}+x^{11}\equiv 1\mod{11}$ has no solution

If $\phi(d)|\phi(n)$ then $d|n$

if $d|n$ then $\phi(dn)=d\phi(n)$

Show that for any prime $p$ and any integer $m$, $m^p + (p − 1)! m$ is divisible by $p$.

Show that $1000000! \equiv 500001 \mod 1000003$

Showing that $-1\not\equiv 5^{n}\pmod{2^k}$.

show that the remainder of $\frac{2^{100}}{23}$ is $2$

for all $n \in {N} : a^n + n | b^n +n$

Show that each number of $100!+1,100!+2,100!+3,...,100!+100$ is composite

Minimize $152207x-81103y$ over the positive integers.

How can I solve this problem : $2^{x} \equiv{2070442609 \cdots 226509} \pmod {6561}$

Show that: $-1 \equiv (-1)^{(p-1)/2}x^2 \pmod p$

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