Fedor Petrov's user avatar
Fedor Petrov's user avatar
Fedor Petrov's user avatar
Fedor Petrov
  • Member for 14 years, 1 month
  • Last seen this week
69 votes
Accepted

integral of a "sin-omial" coefficients=binomial

59 votes

Examples of notably long or difficult proofs that only improve upon existing results by a small amount

54 votes
Accepted

Most elementary proof showing that exponential growth wins against polynomial growth

51 votes

The number $\pi$ and summation by $SL(2,\mathbb Z)$

47 votes
Accepted

Is every polynomial of the form $2x^{2n} -x^n +1$ irreducible over $\mathbb{Z}$?

43 votes
Accepted

Prove that expression is integer

40 votes

Important formulas in combinatorics

40 votes
Accepted

A curious sin-integral

40 votes
Accepted

Does there exist a graph with maximum degree 8, chromatic number 8, clique number 6?

40 votes

Nonequivalent definitions in Mathematics

37 votes
Accepted

How to prove $e^x\left|\int_x^{x+1}\sin(e^t) \,\mathrm d t\right|\le 1.4$?

36 votes

Alternative proofs sought after for a certain identity

33 votes
Accepted

How to prove positivity of determinant for these matrices?

33 votes

Examples of common false beliefs in mathematics

30 votes
Accepted

An equality involving roots of unity which holds most of the times, but not always

30 votes

A conjectural trigonometric identity

30 votes

What is the simplest proof that the density of primes goes to zero?

29 votes

Special rational numbers that appear as answers to natural questions

29 votes

Sum over permutations is 1

28 votes
Accepted

Simultaneous Diophantine approximation of $\sqrt{2}$ and $\sqrt{2\pm \sqrt{3}}$

28 votes
Accepted

A combinatorial identity

28 votes
Accepted

What is the value of this double sum in closed form?

27 votes

What is the minimal size of a partial order that is universal for all partial orders of size n?

27 votes
Accepted

Does greedy circle packing exhaust the measure of every bounded open set in the plane?

26 votes
Accepted

An equality about sin function?

25 votes

Is it possible to create a polynomial $p(x)$ with this relation between $p(0)$ and $p(c)$?

25 votes

Combinatorial identity: $\sum_{i,j \ge 0} \binom{i+j}{i}^2 \binom{(a-i)+(b-j)}{a-i}^2=\frac{1}{2} \binom{(2a+1)+(2b+1)}{2a+1}$

25 votes
Accepted

How to prove that $a + b + 4 \sqrt{1 + a^{2} + b^{2}} \leq 4 \sqrt{a^{2} + b^{2}} + \sqrt{1+b^{2}} + \sqrt{1+a^{2}} + 2 $ for all $a, b > 0$?

24 votes

Examples of eventual counterexamples

24 votes
Accepted

Partitioning a Rectangle into Congruent Isosceles Triangles

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