Question

Infinitely many squares of the form $3a^2 + 1$

score 283 · Answer 1 · 2016-07-18 18:17:48

283

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Infinitely many squares of the form $3a^2 + 1$

Published on 18 Jul 2016 - 18:17

score 34 · Answer 2 · 2016-08-04 13:21:06

34

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find the number of pairs $(a,b)$ where $a,b,n\in\mathbb N$ and $1\le a<b\le n$ and $b|(a^2-1)$ and $a|(b^2-1)$

Published on 04 Aug 2016 - 13:21

score 541 · Answer 3 · 2026-03-27 19:10:16

541

Views

In ℕ⁺, can the sum of three squares equal the sum of two squares?

Published on 27 Mar 2026 - 19:10

score 2.8k · Answer 4 · 2016-08-07 04:14:32

2.8k

Views

How many natural numbers $n$ are there such that $n!+10$ is a perfect square

Published on 07 Aug 2016 - 4:14

score 855 · Answer 5 · 2016-08-07 17:20:39

855

Views

$\frac{1^2+2^2+\cdots+n^2}{n}$ is a perfect square

Published on 07 Aug 2016 - 17:20

score 135 · Answer 6 · 2026-03-27 01:13:20

135

Views

Optimizing continued fraction of square root

Published on 27 Mar 2026 - 1:13

score 708 · Answer 7 · 2016-08-11 02:39:37

708

Views

Why every positive integer can be written as addition of 1 triangle number, 1 square number, and 1 pentagonal number

Published on 11 Aug 2016 - 2:39

score 297 · Answer 8 · 2016-08-20 06:03:09

297

Views

Find ordered positive pairs of integers (x, y) that $x^2y^2-2(x+y)$ is a perfect square.

Published on 20 Aug 2016 - 6:03

score 48.7k · Answer 9 · 2016-08-20 10:01:55

48.7k

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What is the algebraic intuition behind Vieta jumping in IMO1988 Problem 6?

Published on 20 Aug 2016 - 10:01

score 1.3k · Answer 10 · 2016-08-21 11:39:33

1.3k

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Find three consecutive positive integers a,b and c such that a+b is a perfect square and b+c is a perfect cube.

Published on 21 Aug 2016 - 11:39

score 2.2k · Answer 11 · 2026-03-29 13:41:16

2.2k

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Is there any perfect square in the sequence $12,123,1234,12345,...$?

Published on 29 Mar 2026 - 13:41

score 8.3k · Answer 12 · 2026-03-25 17:26:18

8.3k

Views

Math olympiad 1988 problem 6: canonical solution (2) without Vieta jumping

Published on 25 Mar 2026 - 17:26

score 641 · Answer 13 · 2016-08-31 20:06:08

641

Views

When is this true: If $m^2$ is a multiple of N then m is a multiple of N

Published on 31 Aug 2016 - 20:06

score 113 · Answer 14 · 2016-09-01 14:47:17

113

Views

$p(x)=ax^2+bx+c$ sends all integers to perfect squares, whether the polynomial is perfect square?

Published on 01 Sep 2016 - 14:47

score 175 · Answer 15 · 2016-09-02 10:22:36

175

Views

Gower's argument that if $\sqrt{2}$ is rational, then there is an integer that is both even and odd

Published on 02 Sep 2016 - 10:22

List Question

Infinitely many squares of the form $3a^2 + 1$

find the number of pairs $(a,b)$ where $a,b,n\in\mathbb N$ and $1\le a<b\le n$ and $b|(a^2-1)$ and $a|(b^2-1)$

In ℕ⁺, can the sum of three squares equal the sum of two squares?

How many natural numbers $n$ are there such that $n!+10$ is a perfect square

$\frac{1^2+2^2+\cdots+n^2}{n}$ is a perfect square

Optimizing continued fraction of square root

Why every positive integer can be written as addition of 1 triangle number, 1 square number, and 1 pentagonal number

Find ordered positive pairs of integers (x, y) that $x^2y^2-2(x+y)$ is a perfect square.

What is the algebraic intuition behind Vieta jumping in IMO1988 Problem 6?

Find three consecutive positive integers a,b and c such that a+b is a perfect square and b+c is a perfect cube.

Is there any perfect square in the sequence $12,123,1234,12345,...$?

Math olympiad 1988 problem 6: canonical solution (2) without Vieta jumping

When is this true: If $m^2$ is a multiple of N then m is a multiple of N

$p(x)=ax^2+bx+c$ sends all integers to perfect squares, whether the polynomial is perfect square?

Gower's argument that if $\sqrt{2}$ is rational, then there is an integer that is both even and odd

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