List questions from elementary-number-theory

Published on 10 May 2026 - 15:01

50

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Prove or disprove $aB_m-bA_m=[q_n,\cdots,q_m]$

Published on 10 May 2026 - 21:57

52

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Find all n for which $2^n$ divides $3^n-1$

Published on 16 Apr 2026 - 14:24

684

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$n$ has digit sum 100; $2n$ has digit sum 110

Published on 11 May 2026 - 6:34

180

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Find all solutions that satisfy $x^2 + x \equiv 0 \pmod {4000}$

Published on 16 Apr 2026 - 15:54

370

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Set of 6 equations with 6 unknowns

Published on 15 Apr 2026 - 13:14

276

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On existence of positive integer solution of $\binom{x+y}{2}=ax+by$

Published on 10 Apr 2026 - 21:09

134

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Show that rational numbers have the Archimedean property

Published on 12 Apr 2026 - 9:19

744

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If $p \equiv 3 \ (\text{mod} \ 4)$ is a prime, show $(\frac{p-1}{2})! \equiv (-1)^{t} \ (\text{mod} \ p)$

Published on 10 May 2026 - 17:18

301

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A number game for two

Published on 14 May 2026 - 0:31

75

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Prove that if $a \equiv_4 b$ then $3^a \equiv_{10} 3^b$

Published on 14 Apr 2026 - 13:39

112

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Summation problem related to fractional part function

Published on 11 Apr 2026 - 17:13

51

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The five digit number $xy26z$ (each of the letters represents a digit) is divisible by $8$, $9$ and $11$. What is the value of $x$?

Published on 15 Apr 2026 - 22:03

47

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A pair of two digit numbers $ab = x$ and $cd = y$ is called romantic if $a + b = cd$ and $c + d = ab$. Are there even romantic numbers?

Published on 21 Apr 2026 - 15:39

65

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Is any ec-number larger than $73$ the sum of a square and a cube?

Published on 09 Apr 2026 - 5:30

List Question

Let $x(n)=$ product of first $n$ primes.How often is $x(n)$ triangular?

Prove or disprove $aB_m-bA_m=[q_n,\cdots,q_m]$

Find all n for which $2^n$ divides $3^n-1$

$n$ has digit sum 100; $2n$ has digit sum 110

Find all solutions that satisfy $x^2 + x \equiv 0 \pmod {4000}$

Set of 6 equations with 6 unknowns

On existence of positive integer solution of $\binom{x+y}{2}=ax+by$

Show that rational numbers have the Archimedean property

If $p \equiv 3 \ (\text{mod} \ 4)$ is a prime, show $(\frac{p-1}{2})! \equiv (-1)^{t} \ (\text{mod} \ p)$

A number game for two

Prove that if $a \equiv_4 b$ then $3^a \equiv_{10} 3^b$

Summation problem related to fractional part function

The five digit number $xy26z$ (each of the letters represents a digit) is divisible by $8$, $9$ and $11$. What is the value of $x$?

A pair of two digit numbers $ab = x$ and $cd = y$ is called romantic if $a + b = cd$ and $c + d = ab$. Are there even romantic numbers?

Is any ec-number larger than $73$ the sum of a square and a cube?

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