# Oleg567

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 46 Show that the product of two consecutive natural numbers is never a square. 40 Visual explanation of the following statement: 37 If $x \neq 0,y \neq 0,$ then $x^2+xy+y^2$ is … 25 Riddle: 1 question to know if the number is 1, 2 or 3 23 Pi Estimation using Integers

# 7,545 Reputation

 +30 Determining the last two digits of $229^{10} +37^{10}$ +40 Trisecting an angle +10 Show that the number $n$ is divisible by $7$ +10 What is the simplest ellipse that goes through exactly 13 lattice points?

# 9 Questions

 32 Does there exist rational $a,b,c$, such that $\sqrt[3]{1}+\sqrt[3]{2}+\sqrt[3]{4}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}$ 17 Prove that $\sum\limits_{k=0}^{n-1}\dfrac{1}{\cos^2\frac{\pi k}{n}}=n^2$ for odd $n$ 7 How to prove: $a+b+c\le a^2+b^2+c^2$, if $abc=1$? 5 Prove $e^{a_1}+…+e^{a_n}\leqslant e^{b_1}+…+e^{b_n}$, where $a_1+…+a_n=b_1+…+b_n=0$, $|a_j|\leqslant |b_j|$ 4 Generating function of binomial coefficients ${n\choose5}$

# 106 Tags

 113 algebra-precalculus × 28 49 proof-strategy × 2 95 number-theory × 21 48 pi × 5 90 sequences-and-series × 25 47 alternative-proof × 2 87 elementary-number-theory × 18 46 proof-verification 63 diophantine-equations × 14 40 visualization

# 3 Accounts

 Mathematics 7,545 rep 21746 Stack Overflow 158 rep 6 MathOverflow 131 rep 4