How many positive integers n less than 100 have a corresponding integer m divisible by 2 such that the roots of x^2 - nx + m = 0 are consecutive positive integers?
m n
4 3 x^2 - 3x + 2 roots = ( 1, 2)
12 5 x^2 - 5x + 6 roots = ( 2,3)
24 7 x^2 - 7x + 12 roots ( 3,4)
40 9 x^2 - 9x + 20 roots ( 4 , 5)
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3960 99 x^2 - 99x + 1980 roots (44,45)
Number of n = (99 - 3) / 2 + 1 = 48 + 1 = 49
