Question

Can any odd positive integer greater than $3$ be expressed as the sum of $2$ perfect square numbers (excluding $0$) plus $1$ prime number?

score 297 · Answer 1 · 2026-03-26 06:34:45

297

Views

Can any odd positive integer greater than $3$ be expressed as the sum of $2$ perfect square numbers (excluding $0$) plus $1$ prime number?

Published on 26 Mar 2026 - 6:34

score 391 · Answer 2 · 2021-06-06 17:04:21

391

Views

Prove that product of the first $n$ prime numbers plus $1$ is never a perfect square

Published on 06 Jun 2021 - 17:04

score 88 · Answer 3 · 2021-06-10 06:13:19

88

Views

How many natural numbers between $2$ and $60$ have no primitive roots and require at least four squares to be expressed as a sum of squares?

Published on 10 Jun 2021 - 6:13

score 59 · Answer 4 · 2021-06-10 06:31:32

59

Views

Check for perfect square

Published on 10 Jun 2021 - 6:31

score 929 · Answer 5 · 2021-06-10 21:09:27

929

Views

For how many two-element subsets $\{a, b\}$ of the set $\{1, 2, 3, 4, 5, 6, \dots , 36\}$ is the product $ab$ a perfect square?

Published on 10 Jun 2021 - 21:09

score 93 · Answer 6 · 2021-06-15 09:23:41

93

Views

Square numbers in the form of $n^6 + n^4 +1$

Published on 15 Jun 2021 - 9:23

score 124 · Answer 7 · 2021-06-16 16:05:58

124

Views

Given $k$, can we find $n$ such that $d$ is a perfect square

Published on 16 Jun 2021 - 16:05

score 208 · Answer 8 · 2021-06-16 22:23:40

208

Views

Help with Arithmetic Progressions of Perfect Squares

Published on 16 Jun 2021 - 22:23

score 563 · Answer 9 · 2021-06-21 03:10:31

563

Views

A problem about Prime Numbers and Perfect Squares

Published on 21 Jun 2021 - 3:10

score 124 · Answer 10 · 2021-06-21 20:07:32

124

Views

Testing membership for perfect square number

Published on 21 Jun 2021 - 20:07

score 171 · Answer 11 · 2021-06-21 20:12:40

171

Views

Consecutive multiples of squares

Published on 21 Jun 2021 - 20:12

score 178 · Answer 12 · 2021-06-22 23:28:09

178

Views

Are there an infinite number of integers $n$ such that $(3n)(n+1)$ is a perfect square?

Published on 22 Jun 2021 - 23:28

score 197 · Answer 13 · 2021-06-23 18:55:05

197

Views

When is $14k^4 - 6k^2 + 1$ a perfect square?

Published on 23 Jun 2021 - 18:55

score 81 · Answer 14 · 2021-06-30 18:49:42

81

Views

How well $\lfloor\sqrt{x}\rfloor + (x-\lfloor \sqrt{x}\rfloor^2)(2\lfloor \sqrt{x}\rfloor)^{-1}$ approximate $\sqrt{x}$?

Published on 30 Jun 2021 - 18:49

score 47 · Answer 15 · 2021-07-03 16:27:16

47

Views

Is there any number of prime moduli $\ge 5$ such that: $\forall n,\ g(n)\equiv a^2 \bmod p_i \Rightarrow g(n)=k^2$?

Published on 03 Jul 2021 - 16:27

List Question

Can any odd positive integer greater than $3$ be expressed as the sum of $2$ perfect square numbers (excluding $0$) plus $1$ prime number?

Prove that product of the first $n$ prime numbers plus $1$ is never a perfect square

How many natural numbers between $2$ and $60$ have no primitive roots and require at least four squares to be expressed as a sum of squares?

Check for perfect square

For how many two-element subsets $\{a, b\}$ of the set $\{1, 2, 3, 4, 5, 6, \dots , 36\}$ is the product $ab$ a perfect square?

Square numbers in the form of $n^6 + n^4 +1$

Given $k$, can we find $n$ such that $d$ is a perfect square

Help with Arithmetic Progressions of Perfect Squares

A problem about Prime Numbers and Perfect Squares

Testing membership for perfect square number

Consecutive multiples of squares

Are there an infinite number of integers $n$ such that $(3n)(n+1)$ is a perfect square?

When is $14k^4 - 6k^2 + 1$ a perfect square?

How well $\lfloor\sqrt{x}\rfloor + (x-\lfloor \sqrt{x}\rfloor^2)(2\lfloor \sqrt{x}\rfloor)^{-1}$ approximate $\sqrt{x}$?

Is there any number of prime moduli $\ge 5$ such that: $\forall n,\ g(n)\equiv a^2 \bmod p_i \Rightarrow g(n)=k^2$?

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