If a and ...

Question

If $a$ and $b$ are positive integers such that $(a^{2} - b^{2})$ is a prime number, then

a^{2} - b^{2} = (a + b)

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a^{2} - b^{2} = a - b

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a^{2} + b^{2} = a - b

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a^{2} + b^{2} = a + b

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Solution

The correct option is A $a^{2} - b^{2} = (a + b)$
if $a$ and $b$ are positive numbers,
then $(a + b)$ will also be a positive number.

$a^{2} - b^{2} = (a + b) (a - b)$
it is given that ( $a^{2} - b^{2}$ ) is a prime number so, its factors can be only $1$ and itself,
and $(a + b)$ is a positive integer so, $(a - b)$ should be equal to $1$

$a^{2} - b^{2} = (a + b)$

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