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richrow

Member for 4 years, 4 months
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inequality

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Answers

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Score Activity Newest

8

How to find this $\prod_{k=-\infty}^{+\infty}\frac{x^2+(4k+1-y)^2}{x^2+(4k+3-y)^2}$

Aug 22, 2020

6

Show that the elements of the sequence are divisible by $2^n$

Jul 25, 2020

6

Show that $(\binom{p^2}{p} -p ) $ is divisible by $p^5$, for every prime number $p, p\ge 5$

Apr 15, 2019

5

Prove that every tournament contains at least one Hamiltonian path.

Mar 12, 2020

5

Zolotarev's Lemma and Quadratic Reciprocity

Apr 3, 2020

Questions

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Score Activity Newest Views

9

For $a, b, c$ with $a+b+c=0$ prove $\frac15\sum a^5=\frac13\sum a^3\cdot\frac12\sum a^2$ and $\frac17\sum a^7=\frac15\sum a^5\cdot\frac12\sum a^2$

Jan 4, 2022

7

Prime numbers which divide $n^3-3n+1$

Aug 23, 2020

7

Сharacteristic property of polynomials with integer coefficients

Dec 29, 2019

7

Distribution of $\{n^p\alpha\}$ for irrational $\alpha$

May 23, 2020

5

Image of rational numbers under the polynomial map

Feb 1, 2020

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inequality

45

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21

posts

elementary-number-theory

39

Score

17

posts

contest-math

38

Score

25

posts

sequences-and-series

36

Score

17

posts

geometry

34

Score

22

posts

Reputation

+10

Сharacteristic property of polynomials with integer coefficients

+20

Inclusion-exclusion type identity

+10

Prove that $z^{2n} - 2 a^n z^n \cos (nθ) + a^{2n}=\prod_{k=0}^{n-1}\left[z^2-2az\cos\left(\theta+\frac{2\pi k}{n}\right)+a\right]$

+10

Evaluate $\lim_{n \to \infty}\prod_{k=0}^{n} \left(1+\frac{2}{45^{2^k}+45^{-2^k}}\right)$

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