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 162 · Answer 1 · 2020-05-10 20:37:56

162

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 10 May 2020 - 20:37

score 70 · Answer 2 · 2020-06-06 18:08:51

70

Views

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

Published on 06 Jun 2020 - 18:08

score 74 · Answer 3 · 2020-06-21 06:37:43

74

Views

Closest sums of pairs of reciprocals of prime numbers

Published on 21 Jun 2020 - 6:37

score 67 · Answer 4 · 2020-06-28 12:20:18

67

Views

Is there another perfect power?

Published on 28 Jun 2020 - 12:20

score 127 · Answer 5 · 2020-06-30 06:59:43

127

Views

Perfect powers nearest to factorials

Published on 30 Jun 2020 - 6:59

score 82 · Answer 6 · 2020-07-02 18:53:21

82

Views

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

Published on 02 Jul 2020 - 18:53

score 210 · Answer 7 · 2020-07-16 04:49:36

210

Views

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

Published on 16 Jul 2020 - 4:49

score 197 · Answer 8 · 2020-07-19 00:35:46

197

Views

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

Published on 19 Jul 2020 - 0:35

score 246 · Answer 9 · 2020-07-30 10:06:47

246

Views

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

Published on 30 Jul 2020 - 10:06

score 470 · Answer 10 · 2020-07-31 10:39:04

470

Views

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

Published on 31 Jul 2020 - 10:39

score 59 · Answer 11 · 2016-07-12 11:59:59

59

Views

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

Published on 12 Jul 2016 - 11:59

score 66 · Answer 12 · 2016-07-22 08:51:20

66

Views

Why does the modulo affect other terms in the equation?

Published on 22 Jul 2016 - 8:51

score 7.5k · Answer 13 · 2016-08-03 17:52:56

7.5k

Views

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

Published on 03 Aug 2016 - 17:52

score 1k · Answer 14 · 2016-08-04 16:32:08

1k

Views

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

Published on 04 Aug 2016 - 16:32

score 4k · Answer 15 · 2016-08-21 09:51:17

4k

Views

Is this a new method for finding powers?

Published on 21 Aug 2016 - 9:51

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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