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### Questions (23)

 26 31,331,3331, 33331,333331,3333331,33333331 are prime 17 $5^{x}+2^{y}=2^{x}+5^{y} =\frac{7}{10}$ Work out the values of $\frac{1}{x+y}$ 13 Factorial Inequality problem 9 Show that $a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q \implies \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q$ 8 diophantine equations $x^3-2y^3=1$

### Reputation (774)

 +5 31,331,3331, 33331,333331,3333331,33333331 are prime +5 Factorial Inequality problem +5 Prove that $x ^ 3-y ^ 2 = 2$ only has one solution $(3,5)$ +5 Show that $a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q \implies \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q$

### Tags (15)

 0 inequality × 7 0 diophantine-equations × 2 0 number-theory × 3 0 polar-coordinates × 2 0 sequences-and-series × 2 0 functions 0 elementary-number-theory × 2 0 algebra-precalculus 0 geometry × 2 0 induction

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 Mathematics 774 rep 716 Mathematica 104 rep 2