List questions from square-numbers

Published on 24 Jan 2015 - 10:24

472

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Are $121$ and $400$ the only perfect squares of the form $\sum\limits_{k=0}^{n}p^k$?

Published on 26 Jan 2015 - 21:52

3.3k

Views

Can someone help me prove that $\tau(n)$ is odd iff $n$ is a perfect square.

Published on 26 Mar 2026 - 1:03

2k

Views

When is $2^n -7$ a perfect square?

Published on 30 Jan 2015 - 13:47

127

Views

If $x^{1/2}$ is the same as $ \sqrt[2] x$ then why $x^{1/3}$ is not equal to $\sqrt[3] x$?

Published on 30 Jan 2015 - 16:37

406

Views

$d(n)$ is odd iff $n = k^2$

Published on 31 Mar 2026 - 7:28

1.2k

Views

If $ab-1$, $bc-1$, $ca-1$, $ab-a-b+c$, $bc-b-c+a$, $ca-c-a+b$ are perfect squares, then are $ab+a+b-c$, $bc+b+c-a$, $ca+c+a-b$ also perfect squares?

Published on 05 Feb 2015 - 10:46

416

Views

Find the solutions in positive integers $m^2 + 615 =2^n$

Published on 05 Feb 2015 - 13:06

51

Views

A bound on the squares of primes

Published on 12 Feb 2015 - 17:02

157

Views

Numbers in the form $10^n + 1$ with square divisors

Published on 16 Feb 2015 - 16:53

36

Views

Impossibility of Equation

Published on 19 Feb 2015 - 19:04

111

Views

Difference of the difference of consecutive squares

Published on 20 Feb 2015 - 10:05

372

Views

Why can an integer written $2$ times in a row never be a perfect square?

Published on 21 Feb 2015 - 13:42

181

Views

$t$ is a square $\pmod{2^n}$ if and only if $t\equiv 1 \pmod 8$

Published on 21 Feb 2015 - 18:43

459

Views

Looking for all sequences such that $a_i^2+a_j^2=a_k^2+a_l^2$ whenever $i^2+j^2=k^2+l^2$

Published on 28 Mar 2026 - 10:41

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polynomial equation solve in full numbers

Are $121$ and $400$ the only perfect squares of the form $\sum\limits_{k=0}^{n}p^k$?

Can someone help me prove that $\tau(n)$ is odd iff $n$ is a perfect square.

When is $2^n -7$ a perfect square?

If $x^{1/2}$ is the same as $ \sqrt[2] x$ then why $x^{1/3}$ is not equal to $\sqrt[3] x$?

$d(n)$ is odd iff $n = k^2$

If $ab-1$, $bc-1$, $ca-1$, $ab-a-b+c$, $bc-b-c+a$, $ca-c-a+b$ are perfect squares, then are $ab+a+b-c$, $bc+b+c-a$, $ca+c+a-b$ also perfect squares?

Find the solutions in positive integers $m^2 + 615 =2^n$

A bound on the squares of primes

Numbers in the form $10^n + 1$ with square divisors

Impossibility of Equation

Difference of the difference of consecutive squares

Why can an integer written $2$ times in a row never be a perfect square?

$t$ is a square $\pmod{2^n}$ if and only if $t\equiv 1 \pmod 8$

Looking for all sequences such that $a_i^2+a_j^2=a_k^2+a_l^2$ whenever $i^2+j^2=k^2+l^2$

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