chubakueno
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 14 Prove that there are exactly 16 solutions to this problem. 13 Three consecutive integers which are power of prime but not prime 13 Show the identity $\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}=-\frac{a-b}{a+b}\cdot\frac{b-c}{b+c}\cdot\frac{c-a}{c+a}$ 11 Solve this Diophantine Equation: $a^3-b^3 = ab+61$ 8 Compute and find 2009th decimal(2009th digit after the point), without automation, the following sum

### Reputation (3,417)

 +10 software to draw geometry 2D, 3D +5 ODE arising in physics +10 “point earner” problem: cousin of AM-GM +10 Proving $\sqrt{\tan(\alpha)\tan(\beta)+5}+\sqrt{\tan(\alpha)\tan(\gamma)+5}+\sqrt{\tan(\beta)\tan(\gamma)+5}\le4\sqrt{3}$

### Questions (63)

 20 2013 USAMO problem 5 15 Proving that $\frac{n!-1}{2n+7}$ is not an integer when $n>8$ 9 Sums of rising factorial powers 9 Rationalizing expressions 8 If $a+b+c=1$, find the minimum of $\frac{4+3abc}{ab+bc+ac}$

### Tags (77)

 61 elementary-number-theory × 31 16 fractions × 2 36 algebra-precalculus × 34 13 geometry × 8 36 number-theory × 12 13 algebraic-identities 21 contest-math × 11 13 natural-numbers 16 diophantine-equations × 3 10 trigonometry × 14

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