Question

Find the all positive integer solutions $(a,b)$ to $\frac{a^3+b^3}{ab+4}=2020$.

score 342 · Answer 1 · 2026-04-02 03:37:20

342

Views

Find the all positive integer solutions $(a,b)$ to $\frac{a^3+b^3}{ab+4}=2020$.

Published on 02 Apr 2026 - 3:37

score 98 · Answer 2 · 2026-04-02 03:38:25

98

Views

Solutions to Diophantine equation $\frac{1}{n}+\frac{1}{p}=\frac{1}{N}$

Published on 02 Apr 2026 - 3:38

score 77 · Answer 3 · 2020-05-12 07:31:50

77

Views

Prove that for all integers $n$, $3$ does not divide $n^2-5$ using modular arithmetic.

Published on 12 May 2020 - 7:31

score 73 · Answer 4 · 2020-05-12 09:01:33

73

Views

Doubt in understanding polynomial theorem $m-n \mid p(m)-p(n)$

Published on 12 May 2020 - 9:01

score 176 · Answer 5 · 2020-05-14 07:44:54

176

Views

$f(x)$ is monoic polynomial , prove that if $f(k), f(k + 1),..., f(k + p)$ is not divisible by $p + 1$, then $f(x) = 0$ has no rational solution.

Published on 14 May 2020 - 7:44

score 221 · Answer 6 · 2020-05-16 14:41:21

221

Views

Find the smallest value $n$ such that there exists a non-empty subset of any set of n positive integers whose sum is divisible by 1001

Published on 16 May 2020 - 14:41

score 468 · Answer 7 · 2026-03-29 17:11:48

468

Views

Prove any set S of three integers contains a pair $x\neq y$ such that $x^3y-xy^3$ is divisible by 10.

Published on 29 Mar 2026 - 17:11

score 232 · Answer 8 · 2026-03-27 14:21:12

232

Views

Find the number of incongruent solutions

Published on 27 Mar 2026 - 14:21

score 211 · Answer 9 · 2026-03-27 18:26:17

211

Views

On a symmetric equation over the integer lattice that involves the Euler's totient function

Published on 27 Mar 2026 - 18:26

score 56 · Answer 10 · 2020-05-17 23:07:58

56

Views

Proof of divisibility by induction

Published on 17 May 2020 - 23:07

score 400 · Answer 11 · 2020-05-18 13:37:39

400

Views

Consider set $\mathbb{Z}[\sqrt{-5}] = \{a+b\sqrt{5}i : a,b \in \mathbb{Z} \}$ show that it is a ring

Published on 18 May 2020 - 13:37

score 58 · Answer 12 · 2026-03-27 04:58:04

58

Views

Finding conditions such that $4b^2 > a^2 > 3b^2$ and $b \mid (a^2-1)$ imply $b=(a+1)/2$

Published on 27 Mar 2026 - 4:58

score 230 · Answer 13 · 2026-03-26 14:42:15

230

Views

Last 3 digits of $2^{2017}$

Published on 26 Mar 2026 - 14:42

score 112 · Answer 14 · 2020-05-21 15:24:45

112

Views

If $R$ is a UFD, $p(x)\in R[x]$ and $a/b$ is a root of $p(x)$ in the fraction field, then we have $p(x)=(bx-a)q(x)$ for $q(x)\in R[x]$.

Published on 21 May 2020 - 15:24

score 191 · Answer 15 · 2026-03-26 07:59:23

191

Views

About the characterization of solutions of an equation that involves particular values of the Dedekind psi function

Published on 26 Mar 2026 - 7:59

List Question

Find the all positive integer solutions $(a,b)$ to $\frac{a^3+b^3}{ab+4}=2020$.

Solutions to Diophantine equation $\frac{1}{n}+\frac{1}{p}=\frac{1}{N}$

Prove that for all integers $n$, $3$ does not divide $n^2-5$ using modular arithmetic.

Doubt in understanding polynomial theorem $m-n \mid p(m)-p(n)$

$f(x)$ is monoic polynomial , prove that if $f(k), f(k + 1),..., f(k + p)$ is not divisible by $p + 1$, then $f(x) = 0$ has no rational solution.

Find the smallest value $n$ such that there exists a non-empty subset of any set of n positive integers whose sum is divisible by 1001

Prove any set S of three integers contains a pair $x\neq y$ such that $x^3y-xy^3$ is divisible by 10.

Find the number of incongruent solutions

On a symmetric equation over the integer lattice that involves the Euler's totient function

Proof of divisibility by induction

Consider set $\mathbb{Z}[\sqrt{-5}] = \{a+b\sqrt{5}i : a,b \in \mathbb{Z} \}$ show that it is a ring

Finding conditions such that $4b^2 > a^2 > 3b^2$ and $b \mid (a^2-1)$ imply $b=(a+1)/2$

Last 3 digits of $2^{2017}$

If $R$ is a UFD, $p(x)\in R[x]$ and $a/b$ is a root of $p(x)$ in the fraction field, then we have $p(x)=(bx-a)q(x)$ for $q(x)\in R[x]$.

About the characterization of solutions of an equation that involves particular values of the Dedekind psi function

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