# John Marty

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bio website location age member for 1 year, 8 months seen Dec 10 at 6:24 profile views 281

# 58 Questions

 34 Find all real numbers $x$ for which $\frac{8^x+27^x}{12^x+18^x}=\frac76$ 17 Do there exist infinitely many pairs of primes $(p,q)$ such that $pq$ divides $2^{p-1}+2^{q-1}-2$? 11 Show that $4mn-m-n$ can never be a square 9 Functional Equation: a little tricky 9 Elementary Number Theory; prove existence

# 1,660 Reputation

 +30 Can both $x^2 + y+2$ and $y^2+4x$ be squares? +2 Induction proof for Fibonacci numbers +5 Largest number of edges removed from $Q_{10}$ such that the graph always has a Hamiltonian cycle. +5 The camp leader would like to line the children up so that there are at most $2014$ children between any pair of friends.

 15 Can both $x^2 + y+2$ and $y^2+4x$ be squares? 14 Is $83^{27} +1$ a prime number? 7 Sum equal to the product 5 Prove $2$ is only even prime 5 Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$

# 54 Tags

 26 elementary-number-theory × 25 8 inequality × 9 15 square-numbers × 6 6 number-theory × 6 14 prime-numbers × 6 4 geometry × 4 14 factoring × 2 4 soft-question × 2 12 algebra-precalculus × 13 4 education × 2

# 3 Accounts

 Mathematics 1,660 rep 532 English Language & Usage 108 rep 3 Programmers 101 rep