Question

Find $2$ prime numbers one less than a square number, or prove that it is impossible if it cannot be done

score 79 · Answer 1 · 2023-10-28 18:39:32

79

Views

Find $2$ prime numbers one less than a square number, or prove that it is impossible if it cannot be done

Published on 28 Oct 2023 - 18:39

score 72 · Answer 2 · 2023-10-28 21:01:52

72

Views

Find 2 primes with the following property

Published on 28 Oct 2023 - 21:01

score 116 · Answer 3 · 2023-11-04 21:15:02

116

Views

How can i prove that $n^4-2n^3+2n^2-2n+1$ is not a perfect square?

Published on 04 Nov 2023 - 21:15

score 260 · Answer 4 · 2023-11-05 13:17:41

260

Views

What numbers smaller than $28$ can be values of the expression $E=a^2+b^2+c^2-ab-bc-ca$?

Published on 05 Nov 2023 - 13:17

score 4.9k · Answer 5 · 2023-11-16 17:50:24

4.9k

Views

Is enumerating squares via $(a+1)^2 = a^2+(2a+1)$ a new method to find square roots?

Published on 16 Nov 2023 - 17:50

score 165 · Answer 6 · 2026-03-26 02:57:42

165

Views

Is $1 \times 1 + 2 \times 2 + 3 \times 4 + 4 \times 8 = 49$ a coincidence? (Is $\sum_{i=0}^k(i+1)2^i$ ever a square again?)

Published on 26 Mar 2026 - 2:57

score 82 · Answer 7 · 2023-11-23 05:18:16

82

Views

When is $3136 - 6272 n + 3136 n^2 + n^{14}$ a perfect square?

Published on 23 Nov 2023 - 5:18

score 163 · Answer 8 · 2026-03-27 06:07:30

163

Views

When is $x^2+9y^2 \pm y$ a perfect square

Published on 27 Mar 2026 - 6:07

score 70 · Answer 9 · 2023-11-26 09:30:00

70

Views

If $c\ge b\ge a$ and $c\mid a^2,b^2$, and $a$ is the minimal number satisfy $c\mid a^2$, does $a$ necessarily divide $b$?

Published on 26 Nov 2023 - 9:30

score 48 · Answer 10 · 2026-03-26 15:17:17

48

Views

Is there any square harmonic divisor number greater than $1$?

Published on 26 Mar 2026 - 15:17

score 105 · Answer 11 · 2023-11-30 17:55:31

It can be proven that $4^{2000} + 4^x + 4^{2023}$ is the square of an integer for exactly 3 integer values of x. What is the largest such value of x

score 618 · Answer 12 · 2026-03-26 02:56:08

618

Views

Can $1\underbrace{44\cdots4}_{n\text{ times}}$ be a perfect power in other bases?

Published on 26 Mar 2026 - 2:56

score 75 · Answer 13 · 2023-12-16 23:22:13

75

Views

How many different squares are there which are the product of six different integers from 1 to 10 inclusive?

Published on 16 Dec 2023 - 23:22

score 299 · Answer 14 · 2023-12-25 02:15:49

299

Views

If $m$,$n$ are integers, show that $m^2-n^2$ and $m^2+n^2$ cannot both be both perfect squares.

Published on 25 Dec 2023 - 2:15

score 715 · Answer 15 · 2026-03-28 08:49:31

715

Views

Odd square as sum of $9$ distinct odd squares

Published on 28 Mar 2026 - 8:49

List Question

Find $2$ prime numbers one less than a square number, or prove that it is impossible if it cannot be done

Find 2 primes with the following property

How can i prove that $n^4-2n^3+2n^2-2n+1$ is not a perfect square?

What numbers smaller than $28$ can be values of the expression $E=a^2+b^2+c^2-ab-bc-ca$?

Is enumerating squares via $(a+1)^2 = a^2+(2a+1)$ a new method to find square roots?

Is $1 \times 1 + 2 \times 2 + 3 \times 4 + 4 \times 8 = 49$ a coincidence? (Is $\sum_{i=0}^k(i+1)2^i$ ever a square again?)

When is $3136 - 6272 n + 3136 n^2 + n^{14}$ a perfect square?

When is $x^2+9y^2 \pm y$ a perfect square

If $c\ge b\ge a$ and $c\mid a^2,b^2$, and $a$ is the minimal number satisfy $c\mid a^2$, does $a$ necessarily divide $b$?

Is there any square harmonic divisor number greater than $1$?

It can be proven that $4^{2000} + 4^x + 4^{2023}$ is the square of an integer for exactly 3 integer values of x. What is the largest such value of x

Can $1\underbrace{44\cdots4}_{n\text{ times}}$ be a perfect power in other bases?

How many different squares are there which are the product of six different integers from 1 to 10 inclusive?

If $m$,$n$ are integers, show that $m^2-n^2$ and $m^2+n^2$ cannot both be both perfect squares.

Odd square as sum of $9$ distinct odd squares

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