Question

There exist $n$ different integers in the interval $\big(k^n,(k+1)^n\big)$ whose product is a perfect $n$-th power.

score 165 · Answer 1 · 2026-04-14 03:49:28

165

Views

There exist $n$ different integers in the interval $\big(k^n,(k+1)^n\big)$ whose product is a perfect $n$-th power.

Published on 14 Apr 2026 - 3:49

score 71 · Answer 2 · 2026-03-25 12:55:20

71

Views

How can we prove that $3t$ cannot be a perfect cube for any integer $t$ except 9?

Published on 25 Mar 2026 - 12:55

score 75 · Answer 3 · 2026-03-25 12:50:59

75

Views

Closest sums of pairs of reciprocals of prime numbers

Published on 25 Mar 2026 - 12:50

score 69 · Answer 4 · 2026-05-10 22:04:52

69

Views

Is there another perfect power?

Published on 10 May 2026 - 22:04

score 128 · Answer 5 · 2026-03-25 16:06:39

128

Views

Perfect powers nearest to factorials

Published on 25 Mar 2026 - 16:06

score 83 · Answer 6 · 2026-03-25 12:53:03

83

Views

Techniques for solving an equation $f(x)=y^n$ over the integers?

Published on 25 Mar 2026 - 12:53

score 211 · Answer 7 · 2026-03-25 16:03:35

211

Views

Finding an infinite sequence of natural numbers for which any finite partial sum avoids being a perfect power.

Published on 25 Mar 2026 - 16:03

score 198 · Answer 8 · 2026-03-25 12:54:25

198

Views

Can you find a function $\beta(x)$ where if $a+b=n^m$ then $\beta(\frac{a}{b})$ is irrational?

Published on 25 Mar 2026 - 12:54

score 247 · Answer 9 · 2026-03-25 16:01:53

247

Views

Find all $n$ which $7(n^2 + n + 1)$ is perfect $4^{th}$ power.

Published on 25 Mar 2026 - 16:01

score 471 · Answer 10 · 2026-03-25 12:54:25

471

Views

Find all positive integers $n$ for which $1372n^4 - 3 $ is an odd perfect square.

Published on 25 Mar 2026 - 12:54

score 62 · Answer 11 · 2026-04-11 20:56:14

62

Views

how can i rewrite or derive a decimal representation into a diophantine equation?

Published on 11 Apr 2026 - 20:56

score 69 · Answer 12 · 2026-04-10 17:42:45

69

Views

Why does the modulo affect other terms in the equation?

Published on 10 Apr 2026 - 17:42

score 7.5k · Answer 13 · 2026-04-13 17:30:45

7.5k

Views

Finding the greatest power of $2$ less than or equal to a given number

Published on 13 Apr 2026 - 17:30

score 1k · Answer 14 · 2026-04-15 12:34:48

1k

Views

Prove that $\sqrt {2^n-1}$ is irrational for every integer $ n>1$

Published on 15 Apr 2026 - 12:34

score 4k · Answer 15 · 2026-04-10 12:25:37

4k

Views

Is this a new method for finding powers?

Published on 10 Apr 2026 - 12:25

List Question

There exist $n$ different integers in the interval $\big(k^n,(k+1)^n\big)$ whose product is a perfect $n$-th power.

How can we prove that $3t$ cannot be a perfect cube for any integer $t$ except 9?

Closest sums of pairs of reciprocals of prime numbers

Is there another perfect power?

Perfect powers nearest to factorials

Techniques for solving an equation $f(x)=y^n$ over the integers?

Finding an infinite sequence of natural numbers for which any finite partial sum avoids being a perfect power.

Can you find a function $\beta(x)$ where if $a+b=n^m$ then $\beta(\frac{a}{b})$ is irrational?

Find all $n$ which $7(n^2 + n + 1)$ is perfect $4^{th}$ power.

Find all positive integers $n$ for which $1372n^4 - 3 $ is an odd perfect square.

how can i rewrite or derive a decimal representation into a diophantine equation?

Why does the modulo affect other terms in the equation?

Finding the greatest power of $2$ less than or equal to a given number

Prove that $\sqrt {2^n-1}$ is irrational for every integer $ n>1$

Is this a new method for finding powers?

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