Question
If a and b are two odd positive integers, by which of the following integers is (a4 – b4) always divisible ?
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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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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