List questions from elementary-number-theory

Published on 13 Apr 2026 - 17:58

114

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Primes $p=n^6+1$

Published on 26 Mar 2026 - 4:50

269

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Find $21^{1234}\pmod{100}\equiv \ ?$

Published on 11 May 2026 - 3:56

193

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Express $\sum_{a=1}^{p-1} \lfloor{(v+qa)/p}\rfloor$ in closed form.

Published on 16 Apr 2026 - 14:18

1.9k

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Prove that for every n ∈ Z, there exist a, b ∈ Z such that $n = 5a + 2b$.

Published on 05 May 2026 - 7:41

138

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Calculate $1434661\cdot 3785648743-10020304\cdot 54300201$

Published on 15 Apr 2026 - 9:09

108

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Solve in $\mathbb N$: $ 2^x\equiv 1 \bmod{x}$

Published on 16 Apr 2026 - 19:13

73

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should this definition of $a$ divides $b$ be changed?

Published on 12 Apr 2026 - 19:47

101

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prove or disprove: If $c > 0$ and $a < b < c $ , then $a \not \equiv b$ mod $c$

Published on 16 Apr 2026 - 7:30

347

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Solution to a system of quadratic congruences.

Published on 10 May 2026 - 16:11

253

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if $x \equiv y$ (mod $m$), then $ax^2 + bx + c \equiv ay^2 + by + c$ (mod $m$)

Published on 05 May 2026 - 8:48

87

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Solving constraint modulo equation

Published on 12 Apr 2026 - 18:27

89

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$ a , b $ are two odd integers with $\gcd(a,b)=1$. Show that $\gcd(2^a+1,2^b+1)=3$.

Published on 17 Apr 2026 - 8:46

95

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Show that $y^3=4x^2-1$ has no positive integer solutions

Published on 14 Apr 2026 - 2:57

102

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For every $n \in \Bbb Z$, prove there exists $a, b \in \Bbb Z$ such that $n = 5a + 2b$

Published on 16 Apr 2026 - 15:13

List Question

Number of invertible elements in a ring $\mathbb{Z}_n$.

Primes $p=n^6+1$

Find $21^{1234}\pmod{100}\equiv \ ?$

Express $\sum_{a=1}^{p-1} \lfloor{(v+qa)/p}\rfloor$ in closed form.

Prove that for every n ∈ Z, there exist a, b ∈ Z such that $n = 5a + 2b$.

Calculate $1434661\cdot 3785648743-10020304\cdot 54300201$

Solve in $\mathbb N$: $ 2^x\equiv 1 \bmod{x}$

should this definition of $a$ divides $b$ be changed?

prove or disprove: If $c > 0$ and $a < b < c $ , then $a \not \equiv b$ mod $c$

Solution to a system of quadratic congruences.

if $x \equiv y$ (mod $m$), then $ax^2 + bx + c \equiv ay^2 + by + c$ (mod $m$)

Solving constraint modulo equation

$ a , b $ are two odd integers with $\gcd(a,b)=1$. Show that $\gcd(2^a+1,2^b+1)=3$.

Show that $y^3=4x^2-1$ has no positive integer solutions

For every $n \in \Bbb Z$, prove there exists $a, b \in \Bbb Z$ such that $n = 5a + 2b$

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