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I am a student who loves mathematics

# 29 Questions

 10 Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$. 9 Show that $\tan 3x =\frac{ \sin x + \sin 3x+ \sin 5x }{\cos x + \cos 3x + \cos 5x}$ 5 Show that $2^n$ is not a sum of consecutive positive integers [duplicate] 5 Solving $x$ for $y= 3^x-2^x$ 4 Prove that $p-1 \mid p^k(p-2)+1$

# 534 Reputation

 +5 On the Proof of Fundamental Theorem of Linear Programming. +10 Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$. +5 Is the average of all $x$ such that $0 \le x \le 1$ $\forall$ $x \in \mathbb{R}$ equal to $\frac{1}{2}$? +5 Show that $\tan 3x =\frac{ \sin x + \sin 3x+ \sin 5x }{\cos x + \cos 3x + \cos 5x}$

 2 Elementary Geometry 1 Solve a parabola problem? 1 $5^{x}+2^{y}=2^{x}+5^{y} =\frac{7}{10}$ Work out the values of $\frac{1}{x+y}$ 0 In the induction proof for $(1+p)^n \geq 1 + np$, a term is dropped and I don't understand why. 0 Find the values of $a$ and $b$

# 26 Tags

 2 triangle 0 elementary-number-theory × 5 2 geometry 0 sequences-and-series × 3 1 algebra-precalculus × 9 0 inequality × 2 1 exponentiation 0 trigonometry × 2 1 analytic-geometry 0 number-theory × 2

# 4 Accounts

 Mathematics 534 rep 214 Stack Overflow 168 rep 117 TeX - LaTeX 145 rep 5 Programmers 101 rep 2