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Fedor Petrov's user avatar
Fedor Petrov's user avatar
Fedor Petrov's user avatar
Fedor Petrov
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1,152 Answers

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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

51 votes

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

43 votes
Accepted

Prove that expression is integer

40 votes
Accepted

A curious sin-integral

40 votes

Important formulas in combinatorics

39 votes
Accepted

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

39 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

A conjectural trigonometric identity

30 votes
Accepted

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

29 votes

Sum over permutations is 1

29 votes

Special rational numbers that appear as answers to natural questions

29 votes

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

28 votes
Accepted

A combinatorial identity

28 votes
Accepted

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

27 votes
Accepted

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

26 votes
Accepted

An equality about sin function?

26 votes

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

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 $a, b > 0$?

25 votes

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

24 votes

Examples of eventual counterexamples

24 votes
Accepted

Partitioning a Rectangle into Congruent Isosceles Triangles

23 votes

What is the shortest polynomial divisible by $(x-1)(y-1)(x^2y-1)$

23 votes

Proofs that require fundamentally new ways of thinking

22 votes

Sum over permutations is 1

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