Question

Can we reduce the diophantine equation $x^4+4y^4=z^2$ to $x^4+y^4=z^2$ to show there is no nontrivial solution?

score 166 · Answer 1 · 2019-09-06 09:58:08

166

Views

Can we reduce the diophantine equation $x^4+4y^4=z^2$ to $x^4+y^4=z^2$ to show there is no nontrivial solution?

Published on 06 Sep 2019 - 9:58

score 260 · Answer 2 · 2019-09-15 19:40:17

260

Views

Odd power of 2 plus even power of 2, is divisible by 6

Published on 15 Sep 2019 - 19:40

score 46 · Answer 3 · 2019-09-30 21:39:43

46

Views

$f(x)= \frac{1}{x^{2}-3x-4} $The power series expansion at x = 1.

Published on 30 Sep 2019 - 21:39

score 14.3k · Answer 4 · 2014-05-05 23:25:09

14.3k

Views

How many integers between 1 and 10,000 are neither squares nor cubes?

Published on 05 May 2014 - 23:25

score 3.9k · Answer 5 · 2014-05-22 07:37:22

3.9k

Views

To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$

Published on 22 May 2014 - 7:37

score 88 · Answer 6 · 2014-06-17 17:52:43

88

Views

Infinite Perfect power of numbers in a certain form

Published on 17 Jun 2014 - 17:52

score 180 · Answer 7 · 2014-08-16 19:44:05

180

Views

Prove by contradiction that $(n+1)^3 \not= n^3 +(n-1)^3$ for $3$ consecutive positive integers

Published on 16 Aug 2014 - 19:44

score 72 · Answer 8 · 2019-10-20 21:49:38

72

Views

Is there for all $N$ an integer that is the sum of, say, twenty $N$-th powers in two different ways?

Published on 20 Oct 2019 - 21:49

score 124 · Answer 9 · 2019-11-06 18:15:17

124

Views

About primes and their powers in bases $\{2,3,4,5,6,7,8,9,10\}$

Published on 06 Nov 2019 - 18:15

score 86 · Answer 10 · 2019-12-03 07:19:30

86

Views

How to find power of a given number?

Published on 03 Dec 2019 - 7:19

score 815 · Answer 11 · 2026-03-23 03:33:49

815

Views

Find all positive integers satisfying $a^{b^2}=b^a$.

Published on 23 Mar 2026 - 3:33

score 265 · Answer 12 · 2020-03-15 20:59:09

265

Views

Surprising fact about a certain number-theoretic function

Published on 15 Mar 2020 - 20:59

score 294 · Answer 13 · 2020-03-19 23:09:13

294

Views

For any $k \gt 3$, if $n!+k$ is a perfect power then does there exist any $n\gt k$?

Published on 19 Mar 2020 - 23:09

score 408 · Answer 14 · 2020-04-05 19:21:10

408

Views

Sum of perfect powers of n natural numbers

Published on 05 Apr 2020 - 19:21

score 110 · Answer 15 · 2020-04-12 13:21:47

110

Views

How to find the sum of the remainders of a number modulo all the perfect powers less than it?

Published on 12 Apr 2020 - 13:21

List Question

Can we reduce the diophantine equation $x^4+4y^4=z^2$ to $x^4+y^4=z^2$ to show there is no nontrivial solution?

Odd power of 2 plus even power of 2, is divisible by 6

$f(x)= \frac{1}{x^{2}-3x-4} $The power series expansion at x = 1.

How many integers between 1 and 10,000 are neither squares nor cubes?

To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$

Infinite Perfect power of numbers in a certain form

Prove by contradiction that $(n+1)^3 \not= n^3 +(n-1)^3$ for $3$ consecutive positive integers

Is there for all $N$ an integer that is the sum of, say, twenty $N$-th powers in two different ways?

About primes and their powers in bases $\{2,3,4,5,6,7,8,9,10\}$

How to find power of a given number?

Find all positive integers satisfying $a^{b^2}=b^a$.

Surprising fact about a certain number-theoretic function

For any $k \gt 3$, if $n!+k$ is a perfect power then does there exist any $n\gt k$?

Sum of perfect powers of n natural numbers

How to find the sum of the remainders of a number modulo all the perfect powers less than it?

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