Question

Is there a base $b\geq11$ that we obtain a perfect power after we concatenate the first $n$ positive integers of that base?

score 87 · Answer 1 · 2024-02-12 03:30:56

87

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Is there a base $b\geq11$ that we obtain a perfect power after we concatenate the first $n$ positive integers of that base?

Published on 12 Feb 2024 - 3:30

score 47 · Answer 2 · 2024-03-07 19:49:21

47

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Conjecture on digits in arithmetic progression

Published on 07 Mar 2024 - 19:49

score 95 · Answer 3 · 2024-03-08 01:55:10

95

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Conjecture: $\forall n \geq n_0\exists k \geq 0: \gcd(2^k-1, \frac{p_n\#}{6}) = 1$.

Published on 08 Mar 2024 - 1:55

score 39 · Answer 4 · 2024-03-21 10:31:38

39

Views

Is $k=11$ the largest value of $k$ such that $(\lfloor\sqrt{1!+2!+3!+\cdots+k!}\rfloor+1)^{2} - (1!+2!+3!+\cdots+k!)$ is a perfect power?

Published on 21 Mar 2024 - 10:31

score 131 · Answer 5 · 2024-03-27 20:51:41

131

Views

Simpler solution of the Diophantine equation $x^6-y^6=z^2$.

Published on 27 Mar 2024 - 20:51

score 56 · Answer 6 · 2024-03-30 23:01:57

56

Views

Finding all prime powers of the form $\frac{n(n-1)}{10}$

Published on 30 Mar 2024 - 23:01

score 937 · Answer 7 · 2015-01-28 06:41:07

937

Views

Find all primes $p$ such that $p^2-p+1$ is a perfect cube

Published on 28 Jan 2015 - 6:41

score 14.2k · Answer 8 · 2015-02-28 12:04:03

14.2k

Views

Arranging numbers from $1$ to $n$ such that the sum of every two adjacent numbers is a perfect power

Published on 28 Feb 2015 - 12:04

score 182 · Answer 9 · 2015-03-09 15:20:09

182

Views

Determine if a positive integer $x$ is a product of a power of 2 and a power of 5. $f(x) = 2^n \cdot 5^n$

Published on 09 Mar 2015 - 15:20

score 2.6k · Answer 10 · 2015-03-11 16:44:17

2.6k

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Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$

Published on 11 Mar 2015 - 16:44

score 592 · Answer 11 · 2015-03-16 14:02:09

592

Views

How do I prove that $3^n - 3$ is never a square number?

Published on 16 Mar 2015 - 14:02

score 66 · Answer 12 · 2015-03-20 20:22:20

66

Views

Rational number in form $(a^x+b^y)/(c^z+d^w)$

Published on 20 Mar 2015 - 20:22

score 94 · Answer 13 · 2015-04-02 08:36:14

94

Views

There exists a number expressible as the sum of $2015$ $2014$th powers in at least two ways

Published on 02 Apr 2015 - 8:36

score 980 · Answer 14 · 2015-04-03 15:58:47

980

Views

Given a series how do I create a function to describe that series

Published on 03 Apr 2015 - 15:58

score 87 · Answer 15 · 2015-04-04 12:38:38

87

Views

A question about perfect powers

Published on 04 Apr 2015 - 12:38

List Question

Is there a base $b\geq11$ that we obtain a perfect power after we concatenate the first $n$ positive integers of that base?

Conjecture on digits in arithmetic progression

Conjecture: $\forall n \geq n_0\exists k \geq 0: \gcd(2^k-1, \frac{p_n\#}{6}) = 1$.

Is $k=11$ the largest value of $k$ such that $(\lfloor\sqrt{1!+2!+3!+\cdots+k!}\rfloor+1)^{2} - (1!+2!+3!+\cdots+k!)$ is a perfect power?

Simpler solution of the Diophantine equation $x^6-y^6=z^2$.

Finding all prime powers of the form $\frac{n(n-1)}{10}$

Find all primes $p$ such that $p^2-p+1$ is a perfect cube

Arranging numbers from $1$ to $n$ such that the sum of every two adjacent numbers is a perfect power

Determine if a positive integer $x$ is a product of a power of 2 and a power of 5. $f(x) = 2^n \cdot 5^n$

Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$

How do I prove that $3^n - 3$ is never a square number?

Rational number in form $(a^x+b^y)/(c^z+d^w)$

There exists a number expressible as the sum of $2015$ $2014$th powers in at least two ways

Given a series how do I create a function to describe that series

A question about perfect powers

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