Question

On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$

score 163 · Answer 1 · 2026-04-13 01:51:42

163

Views

On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$

Published on 13 Apr 2026 - 1:51

score 73 · Answer 2 · 2026-04-12 04:08:45

73

Views

Solving congruences involving addition for CRT

Published on 12 Apr 2026 - 4:08

score 76 · Answer 3 · 2026-04-12 00:35:28

76

Views

Probability that sum is divisible by $n$

Published on 12 Apr 2026 - 0:35

score 149 · Answer 4 · 2026-04-13 02:52:05

149

Views

Without brute force, how can we show that 1729 is the smallest number that can be expressesed as the sum of two cubes in two different ways?

Published on 13 Apr 2026 - 2:52

score 107 · Answer 5 · 2026-03-25 11:15:02

107

Views

Prove that $d\gt 30000$ when $a_1,a_2.....a_{15}$ are 15 primes on A.P.

Published on 25 Mar 2026 - 11:15

score 119 · Answer 6 · 2026-04-23 13:37:13

119

Views

Finish the exercise to find or count the solutions of the equation $n x^2-\operatorname{rad}(n)=y^3$ over positive integers

Published on 23 Apr 2026 - 13:37

score 45 · Answer 7 · 2026-04-09 17:00:10

45

Views

Is there a cleaner way of solving this number theory problem?

Published on 09 Apr 2026 - 17:00

score 101 · Answer 8 · 2026-04-24 02:27:39

101

Views

Circular reasoning in the hint of proving that if $n$ is a natural number greater than $1$, then $n-1$ is natural number

Published on 24 Apr 2026 - 2:27

score 79 · Answer 9 · 2026-04-17 15:50:06

79

Views

Bill and Fred sent their 30 shirts to the laundry. An elementary number theory problem.

Published on 17 Apr 2026 - 15:50

score 106 · Answer 10 · 2026-04-15 10:05:46

106

Views

Can the integers $n$ expressible as $2a^2-3b^2$ be classified?

Published on 15 Apr 2026 - 10:05

score 899 · Answer 11 · 2026-04-19 12:06:21

899

Views

Find all $x$ such that $4^{27}+4^{1000}+4^{x}$ is a perfect square.

Published on 19 Apr 2026 - 12:06

score 3k · Answer 12 · 2026-04-16 17:26:11

3k

Views

Show that the square of any odd positive integer is of the type 6q or 6q+ 3 or 6q + 5 where q is some integer

Published on 16 Apr 2026 - 17:26

score 108 · Answer 13 · 2026-04-10 04:12:23

108

Views

How to solve the problem on number theory

Published on 10 Apr 2026 - 4:12

score 182 · Answer 14 · 2026-04-15 20:09:44

182

Views

Find $a$, $b$, $c$ such that $\frac{1}{a}+\frac{1}{b}+\frac{2}{c}$ is integer

Published on 15 Apr 2026 - 20:09

score 568 · Answer 15 · 2026-04-12 15:28:47

568

Views

Help with quadratic residues problem.

Published on 12 Apr 2026 - 15:28

List Question

On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$

Solving congruences involving addition for CRT

Probability that sum is divisible by $n$

Without brute force, how can we show that 1729 is the smallest number that can be expressesed as the sum of two cubes in two different ways?

Prove that $d\gt 30000$ when $a_1,a_2.....a_{15}$ are 15 primes on A.P.

Finish the exercise to find or count the solutions of the equation $n x^2-\operatorname{rad}(n)=y^3$ over positive integers

Is there a cleaner way of solving this number theory problem?

Circular reasoning in the hint of proving that if $n$ is a natural number greater than $1$, then $n-1$ is natural number

Bill and Fred sent their 30 shirts to the laundry. An elementary number theory problem.

Can the integers $n$ expressible as $2a^2-3b^2$ be classified?

Find all $x$ such that $4^{27}+4^{1000}+4^{x}$ is a perfect square.

Show that the square of any odd positive integer is of the type 6q or 6q+ 3 or 6q + 5 where q is some integer

How to solve the problem on number theory

Find $a$, $b$, $c$ such that $\frac{1}{a}+\frac{1}{b}+\frac{2}{c}$ is integer

Help with quadratic residues problem.

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