Question

$a+n^2$ is the sum of two perfect squares

score 227 · Answer 1 · 2021-02-05 04:07:42

227

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$a+n^2$ is the sum of two perfect squares

Published on 05 Feb 2021 - 4:07

score 180 · Answer 2 · 2026-03-30 16:09:54

180

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If an arithmetic progression contains a perfect square, then it must contain a perfect square strictly less than ...

Published on 30 Mar 2026 - 16:09

score 46 · Answer 3 · 2021-02-06 13:12:33

46

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Can you prove that if $\mid D_n \mid = m$, where $m$ is odd, then $n$ is a perfect square.

Published on 06 Feb 2021 - 13:12

score 101 · Answer 4 · 2026-03-25 19:03:51

101

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Is there any situation where $x^2 \not= \sqrt{x^4}$

Published on 25 Mar 2026 - 19:03

score 635 · Answer 5 · 2021-02-11 22:31:24

635

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Is it possible to split the natural numbers into a finite number of sets so that no pair of numbers within a set adds up to a square?

Published on 11 Feb 2021 - 22:31

score 130 · Answer 6 · 2021-02-19 07:34:24

130

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How do you prove for all $k$ in the integers, $2-5k$ can never be a perfect square?

Published on 19 Feb 2021 - 7:34

score 810 · Answer 7 · 2021-02-22 07:00:50

810

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$p_{n}$ be the probability that $C+D$ is perfect square. Compute $\lim\limits_{n \to \infty}\left(\sqrt{n} p_{n}\right)$

Published on 22 Feb 2021 - 7:00

score 64 · Answer 8 · 2021-02-25 19:47:37

64

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How do I find a number $\frac{a^4}{4}$ to be added to an odd integer $N$ to make it a Perfect Square?

Published on 25 Feb 2021 - 19:47

score 28 · Answer 9 · 2026-03-26 14:22:53

28

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prove that $\forall k\geqslant1\land k\in\mathbb{Z}.\nexists q\in\mathbb{Z}.q^{2}=(k-i)(k+i)$

Published on 26 Mar 2026 - 14:22

score 113 · Answer 10 · 2021-02-27 00:58:36

113

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How to explain these features of the squares from 01-99?

Published on 27 Feb 2021 - 0:58

score 96 · Answer 11 · 2026-03-30 16:10:03

96

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Is there a tight bound on following binomial summations involving squares on arithmetic progressions?

Published on 30 Mar 2026 - 16:10

score 223 · Answer 12 · 2021-03-01 21:14:13

223

Views

Proving a and b are perfect squares if and only if $\gcd(a,b)$ and $\operatorname{lcm}(a,b)$ are perfect squares

Published on 01 Mar 2021 - 21:14

score 143 · Answer 13 · 2026-03-29 22:44:56

143

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For two odd primes $p<q$, can we deduce positive integers $a,b$ solving $a^2+b^4=pq$ without trial & error (brute force)?

Published on 29 Mar 2026 - 22:44

score 335 · Answer 14 · 2021-03-16 15:28:48

335

Views

Let P denote the product of first n prime numbers (with n > 2). Find all values of $n$ .

Published on 16 Mar 2021 - 15:28

score 147 · Answer 15 · 2021-03-25 02:26:54

147

Views

Square numbers which can be written as two consecutive squares lined up

Published on 25 Mar 2021 - 2:26

List Question

$a+n^2$ is the sum of two perfect squares

If an arithmetic progression contains a perfect square, then it must contain a perfect square strictly less than ...

Can you prove that if $\mid D_n \mid = m$, where $m$ is odd, then $n$ is a perfect square.

Is there any situation where $x^2 \not= \sqrt{x^4}$

Is it possible to split the natural numbers into a finite number of sets so that no pair of numbers within a set adds up to a square?

How do you prove for all $k$ in the integers, $2-5k$ can never be a perfect square?

$p_{n}$ be the probability that $C+D$ is perfect square. Compute $\lim\limits_{n \to \infty}\left(\sqrt{n} p_{n}\right)$

How do I find a number $\frac{a^4}{4}$ to be added to an odd integer $N$ to make it a Perfect Square?

prove that $\forall k\geqslant1\land k\in\mathbb{Z}.\nexists q\in\mathbb{Z}.q^{2}=(k-i)(k+i)$

How to explain these features of the squares from 01-99?

Is there a tight bound on following binomial summations involving squares on arithmetic progressions?

Proving a and b are perfect squares if and only if $\gcd(a,b)$ and $\operatorname{lcm}(a,b)$ are perfect squares

For two odd primes $p<q$, can we deduce positive integers $a,b$ solving $a^2+b^4=pq$ without trial & error (brute force)?

Let P denote the product of first n prime numbers (with n > 2). Find all values of $n$ .

Square numbers which can be written as two consecutive squares lined up

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