1962 AHSME Problems/Problem 36
Problem
If both and
are both integers, how many pairs of solutions are there of the equation
?
Solution
It is obvious that x>10 , thus x=12 , y=3.
Then, let x-8=2n , x-10=2n-2 , it can be written as 2n*(2n-2) = 2^y ,
Also, n (n-1) = 2^y-2 , so, n only can be 2 , y=3, and the answer is .