List questions from elementary-number-theory

Published on 15 Apr 2026 - 17:02

198

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If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.

Published on 14 May 2026 - 20:27

110

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Showing that, if $n,10$ are coprime, then the last $3$ digits of $n^{101}$ will be the same as $n$'s.

Published on 15 Apr 2026 - 2:22

157

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Determine all integers $i$ such that $(i-29)(i+29)$ is a square number

Published on 11 May 2026 - 9:32

79

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Estimating $\sum\limits_{n\leq x} d_3(n)$.

Published on 15 May 2026 - 4:12

93

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Finding out the remainder of $\frac{11^\text{10}-1}{100}$ using modulus

Published on 15 Apr 2026 - 22:41

75

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Partition the set of naturals from $1$ to $16$ into two subsets satisfying certain conditions

Published on 16 Apr 2026 - 11:43

66

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Two sequence relations are equivalent.

Published on 10 May 2026 - 14:45

4.2k

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Which positive integers can NOT be written as a sum of consecutive positive integers

Published on 10 Apr 2026 - 20:06

48

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Is it true that $x^{au} \equiv 1 \pmod p$ $\implies x^{u} \equiv 1 \pmod p$

Published on 16 Apr 2026 - 8:43

252

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How to tell whether function $x^a \mod{b}$ is bijective or not?

Published on 12 Apr 2026 - 13:08

112

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Maximum value of expression $a+b+c$

Published on 10 May 2026 - 17:46

62

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Adding sum of leftmost digits

Published on 14 Apr 2026 - 9:17

41

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When $p(n,m)=\sum\limits_{k=0}^{m}n^{k}$, find $(n,m)$ that $p(n,m)$ is square. $n \in \mathbb N,n>1$.

Published on 17 Apr 2026 - 15:29

140

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Special avatar of Division Algorithm

Published on 14 Apr 2026 - 10:29

List Question

$n\ge 8\,\Rightarrow\, n = 3j + 5k\ $ for $\,j,k,n\in \Bbb N$

If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.

Showing that, if $n,10$ are coprime, then the last $3$ digits of $n^{101}$ will be the same as $n$'s.

Determine all integers $i$ such that $(i-29)(i+29)$ is a square number

Estimating $\sum\limits_{n\leq x} d_3(n)$.

Finding out the remainder of $\frac{11^\text{10}-1}{100}$ using modulus

Partition the set of naturals from $1$ to $16$ into two subsets satisfying certain conditions

Two sequence relations are equivalent.

Which positive integers can NOT be written as a sum of consecutive positive integers

Is it true that $x^{au} \equiv 1 \pmod p$ $\implies x^{u} \equiv 1 \pmod p$

How to tell whether function $x^a \mod{b}$ is bijective or not?

Maximum value of expression $a+b+c$

Adding sum of leftmost digits

When $p(n,m)=\sum\limits_{k=0}^{m}n^{k}$, find $(n,m)$ that $p(n,m)$ is square. $n \in \mathbb N,n>1$.

Special avatar of Division Algorithm

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