Question

Find all positive integers $x,y$ such that $\frac{x^2-1}{xy+1}$ is a non-negative integer.

score 486 · Answer 1 · 2018-05-23 14:18:40

486

Views

Find all positive integers $x,y$ such that $\frac{x^2-1}{xy+1}$ is a non-negative integer.

Published on 23 May 2018 - 14:18

score 23 · Answer 2 · 2026-03-25 03:02:00

23

Views

Practical method for finding a whole number N such that a real number R divided by N is inside a closed interval

Published on 25 Mar 2026 - 3:02

score 44 · Answer 3 · 2018-05-25 12:12:29

44

Views

If $a$ is an odd positive integer $>$ $2$ such that 3 $\not$ | $a$, then $12$ $|$ $(a^2 -$1 ))

Published on 25 May 2018 - 12:12

score 77 · Answer 4 · 2018-05-26 12:33:26

77

Views

I gave a slightly different strong induction proof to $3^{2n+1}+2^{n-1}$, is it correct?

Published on 26 May 2018 - 12:33

score 190 · Answer 5 · 2026-03-25 09:28:58

190

Views

Finishing the task to find the solutions of $\frac{1}{x}-\frac{1}{y}=\frac{1}{\varphi(xy)},$ where $\varphi(n)$ denotes the Euler's totient function

Published on 25 Mar 2026 - 9:28

score 382 · Answer 6 · 2026-03-25 13:13:23

382

Views

How many pairs of adjacent numbers each have a prime number of factors?

Published on 25 Mar 2026 - 13:13

score 99 · Answer 7 · 2026-03-25 13:56:20

99

Views

Proving : For all integers $n\ge 2$ , there exists prime $p$ such that $p\mid n!$ but $p^2$ does not divide $n!$

Published on 25 Mar 2026 - 13:56

score 1.5k · Answer 8 · 2018-05-27 16:01:07

1.5k

Views

Multiplying congruences.

Published on 27 May 2018 - 16:01

score 265 · Answer 9 · 2018-05-27 21:14:02

265

Views

To what extend does shared roots imply divisibility of polynomials?

Published on 27 May 2018 - 21:14

score 223 · Answer 10 · 2018-05-28 16:52:23

223

Views

Why do remainders on each side of the equation have to be equal?

Published on 28 May 2018 - 16:52

score 18 · Answer 11 · 2026-03-25 09:35:48

18

Views

Precentage Calculation on two objects of different sizes that returns the same result

Published on 25 Mar 2026 - 9:35

score 188 · Answer 12 · 2018-05-31 11:26:28

188

Views

Divisibility of a 7-digit number by 21

Published on 31 May 2018 - 11:26

score 49 · Answer 13 · 2026-03-25 02:59:21

49

Views

Finding integral values of $3$ different variables.

Published on 25 Mar 2026 - 2:59

score 38 · Answer 14 · 2018-05-31 23:00:21

38

Views

Integers $x,y$ so that $2y^2+3\mid x^2-2$

Published on 31 May 2018 - 23:00

score 420 · Answer 15 · 2026-03-25 07:05:57

420

Views

${3^n\choose k}$ is divisible by $3$?

Published on 25 Mar 2026 - 7:05

List Question

Find all positive integers $x,y$ such that $\frac{x^2-1}{xy+1}$ is a non-negative integer.

Practical method for finding a whole number N such that a real number R divided by N is inside a closed interval

If $a$ is an odd positive integer $>$ $2$ such that 3 $\not$ | $a$, then $12$ $|$ $(a^2 -$1 ))

I gave a slightly different strong induction proof to $3^{2n+1}+2^{n-1}$, is it correct?

Finishing the task to find the solutions of $\frac{1}{x}-\frac{1}{y}=\frac{1}{\varphi(xy)},$ where $\varphi(n)$ denotes the Euler's totient function

How many pairs of adjacent numbers each have a prime number of factors?

Proving : For all integers $n\ge 2$ , there exists prime $p$ such that $p\mid n!$ but $p^2$ does not divide $n!$

Multiplying congruences.

To what extend does shared roots imply divisibility of polynomials?

Why do remainders on each side of the equation have to be equal?

Precentage Calculation on two objects of different sizes that returns the same result

Divisibility of a 7-digit number by 21

Finding integral values of $3$ different variables.

Integers $x,y$ so that $2y^2+3\mid x^2-2$

${3^n\choose k}$ is divisible by $3$?

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