If a and b are two odd positive integers, by which of the following integers is (a4 – b4) always divisible ?
Options:
A . 3
B . 6
C . 8
D . 12
Answer: Option C Answer: (c) $a^4 - b^4 = (a - b) (a + b) (a^2 + b^2)$, Where a and b are odd positive integers. If two positive integers are odd, then their sum, difference and sum of their squares are always even. ∴ (a - b) (a + b) and $(a^2 + b^2)$ are divisible by 2. Hence (a - b) (a + b) x $(a^2 + b^2) = a^4 - b^4$ is always divisible by $2^3 = 8$
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