Question

Find all $n\in\mathbb N$, $n>3$ such that $p(n)=2n+16$, where $p(n)$ is the product of all the prime numbers less than $n$.

score 284 · Answer 1 · 2026-04-17 14:42:34

284

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Find all $n\in\mathbb N$, $n>3$ such that $p(n)=2n+16$, where $p(n)$ is the product of all the prime numbers less than $n$.

Published on 17 Apr 2026 - 14:42

score 168 · Answer 2 · 2026-04-14 20:50:54

168

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nonlinear diophantine equation $x^2+y^2=z^2$

Published on 14 Apr 2026 - 20:50

score 3.3k · Answer 3 · 2026-04-13 02:46:04

3.3k

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Solve $x^2+2=y^3$ using infinite descent?

Published on 13 Apr 2026 - 2:46

score 31 · Answer 4 · 2026-04-15 14:41:59

31

Views

Number of solutions for (a-x)(b-y)-1=0

Published on 15 Apr 2026 - 14:41

score 193 · Answer 5 · 2026-04-10 19:52:28

193

Views

Diophantine equation using Pell's equation

Published on 10 Apr 2026 - 19:52

score 825 · Answer 6 · 2026-04-09 01:42:02

825

Views

A conjecture about Pythagorean triples

Published on 09 Apr 2026 - 1:42

score 82 · Answer 7 · 2026-04-12 20:17:26

For a Pythagorean triple $a, b, c \in N$, if a is even and a, b, c have no common factors, prove that $c-a$ and $c+a$ are perfect squares.

score 70 · Answer 8 · 2026-04-09 15:20:20

70

Views

Equation in rational numbers

Published on 09 Apr 2026 - 15:20

score 66 · Answer 9 · 2026-04-16 18:09:13

66

Views

Given the sum of a geometric progression and the number of terms, can we recover the progression?

Published on 16 Apr 2026 - 18:09

score 638 · Answer 10 · 2026-04-17 00:06:44

638

Views

If $(m,n)\in\mathbb Z_+^2$ satisfies $3m^2+m = 4n^2+n$ then $(m-n)$ is a perfect square.

Published on 17 Apr 2026 - 0:06

score 80 · Answer 11 · 2026-04-15 01:06:51

80

Views

How to solve diophantine equation $\frac{x^p-y^p}{x-y}=n$

Published on 15 Apr 2026 - 1:06

score 253 · Answer 12 · 2026-04-15 16:09:55

253

Views

How to solve equations like $x^2+y^2=2004^{2005}$?

Published on 15 Apr 2026 - 16:09

score 290 · Answer 13 · 2026-04-17 07:22:49

290

Views

Integer solutions of $ x^3+y^3+z^3=(x+y+z)^3 $

Published on 17 Apr 2026 - 7:22

score 101 · Answer 14 · 2026-04-11 08:20:35

101

Views

Diophantine Equation with 15th power

Published on 11 Apr 2026 - 8:20

score 85 · Answer 15 · 2026-04-14 10:56:25

85

Views

Can 11 be represented by $a^2 - 3b^2$ where a and b are integers?

Published on 14 Apr 2026 - 10:56

List Question

Find all $n\in\mathbb N$, $n>3$ such that $p(n)=2n+16$, where $p(n)$ is the product of all the prime numbers less than $n$.

nonlinear diophantine equation $x^2+y^2=z^2$

Solve $x^2+2=y^3$ using infinite descent?

Number of solutions for (a-x)(b-y)-1=0

Diophantine equation using Pell's equation

A conjecture about Pythagorean triples

For a Pythagorean triple $a, b, c \in N$, if a is even and a, b, c have no common factors, prove that $c-a$ and $c+a$ are perfect squares.

Equation in rational numbers

Given the sum of a geometric progression and the number of terms, can we recover the progression?

If $(m,n)\in\mathbb Z_+^2$ satisfies $3m^2+m = 4n^2+n$ then $(m-n)$ is a perfect square.

How to solve diophantine equation $\frac{x^p-y^p}{x-y}=n$

How to solve equations like $x^2+y^2=2004^{2005}$?

Integer solutions of $ x^3+y^3+z^3=(x+y+z)^3 $

Diophantine Equation with 15th power

Can 11 be represented by $a^2 - 3b^2$ where a and b are integers?

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