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mathlove
  • Member for 10 years, 10 months
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24 votes
4 answers
2k views

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

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

33 votes
3 answers
4k views

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

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

4 votes
3 answers
494 views

Repeating an operation infinitely makes any convex $n$-gon a regular $n$-gon?

24 votes
4 answers
2k views

Does this sequence always give an integer?

5 votes
0 answers
766 views

Conjectures on perfect squares

0 votes
1 answer
557 views

Permutations of letters under some conditions

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

9 votes
1 answer
544 views

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

2 votes
2 answers
658 views

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

13 votes
0 answers
635 views

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

5 votes
1 answer
523 views

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

2 votes
2 answers
770 views

Examples that the Fermat-Catalan conjecture does not cover

4 votes
0 answers
271 views

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

3 votes
1 answer
343 views

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

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 $(a,b,c)=(1,2,3)$?

10 votes
3 answers
2k views

On maximal regular polyhedra inscribed in a regular polyhedron

6 votes
0 answers
248 views

On simple normality to co-prime bases

11 votes
0 answers
723 views

Making a convex polyhedron with two sheets of paper

13 votes
0 answers
543 views

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

5 votes
2 answers
1k views

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

0 votes
2 answers
230 views

Finding the min of a sequence related with factorials

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 $(n,k)$

1 vote
0 answers
242 views

Multiplicative semi-magic squares

4 votes
1 answer
563 views

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

7 votes
1 answer
2k views

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

12 votes
3 answers
1k views

A special tessellation

9 votes
3 answers
416 views

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