User mathlove

22 votes

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Can we simplify $\int_{0}^{\infty}\frac{{\sin}^px}{x^q}dx$?

answered Dec 3, 2013 at 15:25

4 votes

Primality test for generalized Fermat numbers

answered Oct 7, 2018 at 6:09

3 votes

Primality test for specific class of $N=8kp^n-1$

answered Jun 2, 2020 at 12:18

2 votes

On the nearest-square function and the quantity $m^2 - p^k$ where $p^k m^2$ is an odd perfect number

answered Nov 22, 2020 at 12:35

2 votes

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About the set of all the solutions $\mathbf x=(x_1,x_2,\cdots,x_m)$ to $\sum_{j=1}^m\frac{1}{x_j}=\frac1n$

answered Oct 6, 2013 at 14:37

2 votes

If $\left(1^a+2^a+\cdots+n^{a}\right)^b=1^c+2^c+\cdots+n^c$ for some $n$, then $(a,b,c)=(1,2,3)$?

answered Oct 12, 2013 at 12:50

2 votes

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

answered Oct 23, 2021 at 10:30

1 vote

Accepted

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

answered Dec 24, 2021 at 5:17

1 vote

Accepted

An inequality about the sum of some unit fractions with a property

answered Oct 29, 2013 at 16:52

1 vote

Numbers $n$ such that the sum of the divisors of $n$ is a nontrivial power

answered Apr 2, 2015 at 11:56

1 vote

Accepted

On the Diophantine equation $m^2 - p^k = 2^r t$, where $r \geq 2$ and $\gcd(2,t)=1$

answered Jun 28, 2021 at 10:00

1 vote

Non-trivial solution to $\sum^{n}_{i=1}\sum^{n}_{j=1,j\ne i}(x_{i})^{(x_j)}=(\sum^{n}_{i=1}x_i)^{(\sum^{n}_{i=1}x_i)}$

answered Jul 2, 2021 at 7:12

0 votes

Accepted

About the sum of the first half and the latter half of the cyclic numbers of a repeating decimal

answered Oct 27, 2013 at 14:59

0 votes

Finding the min of a sequence related with factorials

answered Dec 4, 2013 at 6:39

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14 Answers

Can we simplify $\int_{0}^{\infty}\frac{{\sin}^px}{x^q}dx$?

Primality test for generalized Fermat numbers

Primality test for specific class of $N=8kp^n-1$

On the nearest-square function and the quantity $m^2 - p^k$ where $p^k m^2$ is an odd perfect number

About the set of all the solutions $\mathbf x=(x_1,x_2,\cdots,x_m)$ to $\sum_{j=1}^m\frac{1}{x_j}=\frac1n$

If $\left(1^a+2^a+\cdots+n^{a}\right)^b=1^c+2^c+\cdots+n^c$ for some $n$, then $(a,b,c)=(1,2,3)$?

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

An inequality about the sum of some unit fractions with a property

Numbers $n$ such that the sum of the divisors of $n$ is a nontrivial power

On the Diophantine equation $m^2 - p^k = 2^r t$, where $r \geq 2$ and $\gcd(2,t)=1$

Non-trivial solution to $\sum^{n}_{i=1}\sum^{n}_{j=1,j\ne i}(x_{i})^{(x_j)}=(\sum^{n}_{i=1}x_i)^{(\sum^{n}_{i=1}x_i)}$

About the sum of the first half and the latter half of the cyclic numbers of a repeating decimal

Finding the min of a sequence related with factorials