# Lazar Ljubenović

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bio website location Nish, Serbia age 19 member for 2 years, 2 months seen yesterday profile views 250

(my about me is currently blank)

# 63 Questions

 14 Prove that line through intersection of line through foots of heights and opposite line and orthocenter is perpendicular to median. 12 Prove that integer $n$ exists such that $n^2$ begins with $201120122013$. 12 Prove that $x_1^2+x_2^2+x_3^2=1$ yields $\sum_{i=1}^{3}\frac{x_i}{1+x_i^2} \le \frac{3\sqrt{3}}{4}$ 11 Prove $\sqrt[n]{m}\leq\sqrt[3]{3}\lor\sqrt[m]{n}\leq\sqrt[3]{3}$ for $n,m\in\mathbb{N}>1$. 11 Prove that $n^{2003}+n+1$ is composite for every $n\in \mathbb{N} \backslash\{1\}$

# 1,076 Reputation

 +5 The inverse of a matrix (main diagonal $2$, left and right of it $-1$) +5 System $a+b+c=4$, $a^2+b^2+c^2=8$. find all possible values for $c$. +5 Part from “Regular polytopes” which I don't understand +5 Evaluating $\lim_{n\to\infty} \left({1\over1\cdot2\cdot3}+{1\over2\cdot3\cdot4}+\cdots+{1\over(n-1)\cdot n\cdot(n+1)}\right)$

 6 Solve this: $\sqrt{x^2+3x+6}+\sqrt{2x^2-1}=3x+1$ 2 How to compute the area of the shadow? 2 How to calculate the number of pieces in the border of a puzzle? 2 How to show this equation is true? 2 How can I plot the point of $y=\sin(x)$?

# 44 Tags

 12 homework × 5 3 calculus × 3 8 algebra-precalculus × 8 2 combinatorics × 8 6 geometry × 15 2 puzzle 6 trigonometry × 10 1 triangle × 3 3 elementary-number-theory × 19 1 logarithms × 3

# 6 Accounts

 Mathematics 1,076 rep 419 TeX - LaTeX 220 rep 14 Stack Overflow 148 rep 7 Japanese Language 101 rep 2 Anime & Manga 101 rep 1