If a and b are two odd positive integers, by which of the following integers is (a4 – b4) always divisible ?
3
6
8
12
Correct Option: C
We know that , a4 – b4 = (a2)2 – (b2)2 = (a2 + b2) (a2 − b2) = (a2 + b2) (a + b) (a – b) Let a = 3, b = 1 ∴ Required number = ( 3 + 1 ) ( 3 – 1 ) = 4 x 2 = 8
