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mathlove
  • Member for 10 years, 10 months
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38 votes
3 answers
5k views

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

34 votes
4 answers
2k views

About the ratio of the areas of a convex pentagon and the inner pentagon made by the five diagonals

33 votes
3 answers
4k views

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

24 votes
4 answers
2k views

Letting $S(m)$ be the digit sum of $m$, then $\lim_{n\to\infty}S(3^n)=\infty$?

24 votes
4 answers
2k views

Does this sequence always give an integer?

22 votes
1 answer
10k views

Prove that ${\sqrt2}^{\sqrt2}$ is an irrational number without using a theorem

20 votes
1 answer
876 views

Tetrahedra passing through a hole

17 votes
5 answers
1k views

Proving that every term of the sequence is an integer

17 votes
1 answer
919 views

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

14 votes
3 answers
1k views

What is the max of $n$ such that $\sum_{i=1}^n\frac{1}{a_i}=1$ where $2\le a_1\lt a_2\lt \cdots\lt a_n\le m$?

13 votes
2 answers
2k views

Proving $\sum_{k=0}^{2m}(-1)^k{\binom{2m}{k}}^3=(-1)^m\binom{2m}{m}\binom{3m}{m}$

13 votes
0 answers
543 views

If $\beta=0.{a_1}^{k}{a_2}^{k}{a_3}^{k}\cdots\in\mathbb Q$, then $\alpha=0.a_1a_2a_3\cdots\in\mathbb Q$?

13 votes
0 answers
635 views

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

12 votes
3 answers
1k views

A special tessellation

11 votes
0 answers
723 views

Making a convex polyhedron with two sheets of paper

10 votes
3 answers
2k views

On maximal regular polyhedra inscribed in a regular polyhedron

9 votes
1 answer
544 views

What is the shape of the $n$-gon which gives the maximum of a function?

9 votes
3 answers
416 views

About a solid which satisfies $\sum_{i=1}^{n}x_i=0, |x_i|\le1\ (i=1,2,\cdots,n)$

8 votes
0 answers
508 views

Proving a proposition which leads the irrationality of $\frac{\zeta(5)}{\zeta(2)\zeta(3)}$

7 votes
1 answer
492 views

Finding the min of $m$ such that $k = \pm 1^n \pm 2^n \pm 3^n \pm \cdots \pm m^n$ for a given pair $(n,k)$

7 votes
1 answer
2k views

The number of distinct prime factors of $n\in\mathbb N$

6 votes
0 answers
248 views

On simple normality to co-prime bases

5 votes
1 answer
433 views

A problem related with 'Postage stamp problem'

5 votes
3 answers
1k views

Finding an invisible circle by drawing another line

5 votes
2 answers
2k views

Solving $x^k+(x+1)^k+(x+2)^k+\cdots+(x+k-1)^k=(x+k)^k$ for $k\in\mathbb N$

5 votes
2 answers
1k views

About two 'negative' continued fractions whose sum equals $1$

5 votes
0 answers
766 views

Conjectures on perfect squares

5 votes
1 answer
523 views

Permutation polynomials mod $p$ of the form $(x+1)^n-x^n$

4 votes
0 answers
271 views

How many points does 'the-most-point-contained-circle' contain at least?

4 votes
1 answer
563 views

About the inscribed sphere and the exspheres of a $n$-dimensional simplex