If a and b are integers, and a^2 - b^2 = 15, what could be the values of a and b ?
Correct: A
The given equation a^2 - b^2 = 15 can be rewritten as (a + b)(a - b) = 15. Since 15 is a product of 15*1 or 5*3 (ignoring negative factors), possible values for (a + b) and (a - b) are (15, 1) or (5, 3). Solving simultaneously: for (a + b) = 15 and (a - b) = 1, adding both equations gives 2a = 16, a = 8, then 8 + b = 15, b = 7. For (a + b) = 5 and (a - b) = 3, adding both gives 2a = 8, a = 4, then 4 + b = 5, b = 1. Hence one of the possible pairs could be a = 4, b = 1.