If a and b are positive integers such that a^2 - b^2 = 21, what is the value of a?
Correct: A
a^2 - b^2 = (a+b)(a-b) = 21. Since a and b are positive integers, a+b and a-b must be integer factors of 21. The pairs of factors of 21 are (1, 21) and (3, 7). If a+b = 21 and a-b = 1, then 2a = 22, so a = 11 and b = 10. If a+b = 7 and a-b = 3, then 2a = 10, so a = 5 and b = 2. Since the question is asking for one possible value for a, it is likely the smaller a=5