You may discuss these problems with me, or with other students in this class, but with no one else. You should write legibly, and carefully justify your answers.
(1) ) If n is a (fixed) positive integer what is the number of solutions (x,y) (with x and y positive integers) to the equation
1/x + 1/y = 1/n .
Carefully explain your reasoning. (Hint: Compute (x-n)⋅(y-n) .)
(2) Let n = 3t-1. Show that 2n ≡ -1 (mod 3t )
(3) If p is a prime show that every prime factor of 2p − 1 is larger than p