Question

Why is $\sum_{j^2\leq \sqrt x} \mu(j)[\frac x {j^2}]=x\sum_{j^2\leq \sqrt x}\frac {\mu(j)} {j^2}+ O(\sqrt x)$?

score 116 · Answer 1 · 2026-03-29 07:33:43

116

Views

Why is $\sum_{j^2\leq \sqrt x} \mu(j)[\frac x {j^2}]=x\sum_{j^2\leq \sqrt x}\frac {\mu(j)} {j^2}+ O(\sqrt x)$?

Published on 29 Mar 2026 - 7:33

score 85 · Answer 2 · 2026-03-29 13:30:07

85

Views

A simple problem on congruences.

Published on 29 Mar 2026 - 13:30

score 108 · Answer 3 · 2026-04-10 09:13:45

108

Views

Landau's comment on validity of Goldbach's conjecture

Published on 10 Apr 2026 - 9:13

score 51 · Answer 4 · 2026-03-28 20:12:19

51

Views

A problem on simple congruences.

Published on 28 Mar 2026 - 20:12

score 32 · Answer 5 · 2026-03-28 09:49:05

32

Views

Prove that $kn+r$ isn't divisible by $k$ if $r$ isn't divisible by $k$ and $k$,$n$ and $r$ are integers.

Published on 28 Mar 2026 - 9:49

score 60 · Answer 6 · 2026-03-26 01:46:22

60

Views

How to make the arithmetic progression contain infinitely many primes by adding a rational number to common difference?

Published on 26 Mar 2026 - 1:46

score 1.5k · Answer 7 · 2018-02-11 20:09:57

1.5k

Views

Sum of products of elements of nonempty subsets of A set

Published on 11 Feb 2018 - 20:09

score 180 · Answer 8 · 2026-04-09 00:26:55

180

Views

Fundamental solution to specific Pell equation

Published on 09 Apr 2026 - 0:26

score 59 · Answer 9 · 2026-03-29 00:25:51

59

Views

closed form expression for sum of sequence of tuples that resemble a binary counter

Published on 29 Mar 2026 - 0:25

score 48 · Answer 10 · 2026-03-28 18:13:41

48

Views

Proof for $\gcd$ operation, with out using technique of showing counter-example.

Published on 28 Mar 2026 - 18:13

score 176 · Answer 11 · 2026-03-29 15:52:14

176

Views

Covering systems for integers vs. natural numbers

Published on 29 Mar 2026 - 15:52

score 975 · Answer 12 · 2026-04-06 11:54:05

975

Views

What are the different subjects in number theory to do research?

Published on 06 Apr 2026 - 11:54

score 52 · Answer 13 · 2026-03-29 09:42:41

52

Views

Irrationality of sum of b-ary interpretations of positive rational number

Published on 29 Mar 2026 - 9:42

score 79 · Answer 14 · 2026-03-28 20:20:49

79

Views

For given odd prime $q$, does there exist a prime $p$ such that $q$ is a primitive root mod $p$?

Published on 28 Mar 2026 - 20:20

score 112 · Answer 15 · 2026-03-29 06:49:13

112

Views

Find $a, b \in \mathbb{N} $ such that $\frac{1}{a}+\frac{1}{b} +\frac{1}{(a,b)}+\frac{1}{[a,b]}=\frac{1}{2}$

Published on 29 Mar 2026 - 6:49

List Question

Why is $\sum_{j^2\leq \sqrt x} \mu(j)[\frac x {j^2}]=x\sum_{j^2\leq \sqrt x}\frac {\mu(j)} {j^2}+ O(\sqrt x)$?

A simple problem on congruences.

Landau's comment on validity of Goldbach's conjecture

A problem on simple congruences.

Prove that $kn+r$ isn't divisible by $k$ if $r$ isn't divisible by $k$ and $k$,$n$ and $r$ are integers.

How to make the arithmetic progression contain infinitely many primes by adding a rational number to common difference?

Sum of products of elements of nonempty subsets of A set

Fundamental solution to specific Pell equation

closed form expression for sum of sequence of tuples that resemble a binary counter

Proof for $\gcd$ operation, with out using technique of showing counter-example.

Covering systems for integers vs. natural numbers

What are the different subjects in number theory to do research?

Irrationality of sum of b-ary interpretations of positive rational number

For given odd prime $q$, does there exist a prime $p$ such that $q$ is a primitive root mod $p$?

Find $a, b \in \mathbb{N} $ such that $\frac{1}{a}+\frac{1}{b} +\frac{1}{(a,b)}+\frac{1}{[a,b]}=\frac{1}{2}$

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