List questions from number-theory

Published on 08 Apr 2026 - 22:50

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Consider $T$ = $9 \times 99 \times 999 \times 9999 \times \cdots \times \underbrace{999....9}_{2015 \:nines}$

Published on 11 Apr 2026 - 6:57

312

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A high school Olympiad problem

Published on 11 Apr 2026 - 14:50

136

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Find all pairs $(n,k)$

Published on 10 Apr 2026 - 12:20

145

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Equivalence of quadratic forms and general advice about "Number Theory" (by Borevich-Shafarevich)

Published on 09 Apr 2026 - 2:01

123

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$\sum_{y=0}^{p-1 } (\frac{y^2 - b^{-1}}{p}) =-1$

Published on 09 Apr 2026 - 2:54

94

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Is there any approach proof for Legendre conjecture or it is completed solved?

Published on 25 Mar 2026 - 4:10

942

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Pattern for square numbers

Published on 31 Mar 2026 - 16:03

132

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Integral of Gamma Functions

Published on 10 Apr 2026 - 14:59

87

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Estimating $\sum\limits_{2\le n,m\le X}\frac{\Lambda(n)\Lambda(m)}{(nm)^\sigma\log(n)\log(m)}$

Published on 25 Mar 2026 - 20:35

204

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Heuristics on the asymptotic behaviour of the divisor funcion

Published on 09 Apr 2026 - 2:01

70

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Unexpected number appears

Published on 05 Apr 2026 - 14:34

216

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Solving Linear Congruence Equations

Published on 24 Mar 2026 - 23:42

3k

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Totally ramified extensions of $\mathbb{Q}_p$

Published on 06 Apr 2026 - 18:47

62

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If $f = a_0 + a_1t + \cdots\in\mathbb{Z}_p[[t]]$ has $p\mid a_0$ but $p\nmid f$, could $1/f$ have bounded denominators in $\mathbb{Q}_p[[t]]$?

Published on 25 Mar 2026 - 18:50

List Question

Proof relating to the gcd of two numbers

Consider $T$ = $9 \times 99 \times 999 \times 9999 \times \cdots \times \underbrace{999....9}_{2015 \:nines}$

A high school Olympiad problem

Find all pairs $(n,k)$

Equivalence of quadratic forms and general advice about "Number Theory" (by Borevich-Shafarevich)

$\sum_{y=0}^{p-1 } (\frac{y^2 - b^{-1}}{p}) =-1$

Is there any approach proof for Legendre conjecture or it is completed solved?

Pattern for square numbers

Integral of Gamma Functions

Estimating $\sum\limits_{2\le n,m\le X}\frac{\Lambda(n)\Lambda(m)}{(nm)^\sigma\log(n)\log(m)}$

Heuristics on the asymptotic behaviour of the divisor funcion

Unexpected number appears

Solving Linear Congruence Equations

Totally ramified extensions of $\mathbb{Q}_p$

If $f = a_0 + a_1t + \cdots\in\mathbb{Z}_p[[t]]$ has $p\mid a_0$ but $p\nmid f$, could $1/f$ have bounded denominators in $\mathbb{Q}_p[[t]]$?

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