Suppose that a and b are integers such that 3b = 8 - 2a. How many of the first six positive integers must be divisors of 2b + 30?
b = (8 - 2a) / 3
For b to be an integer, a must be 1 , 4 , 7 , 10 ....
2b + 30 = 2 ( b + 15) = 2 [ (8 -2a) / 3 + 15 ] = 2 [ 53 - 2a] / 3
Divisors = 1 , 2 , 6
