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

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$a $ and $ b$ are positive integers and $a^2 - b^2$ is a prime number. Since, $a^2 - b^2 = (a+ b) (a - b)$ product of two numbers. $	herefore$ Either $a + b = 1$ or $a - b = 1$ Case I : $a + b = 1 \Rightarrow $ Either $a = 0$ or $b = 0$ then $a^2 - b^2 = 1$ or $-1$ which is not a prime number. $ 	herefore$ This case is not possible Case II : $a - b = 1 ightarrow a$ and $b$ can be taken anything with $b < a$ . ln this case $a^2 - b^2 = a + b$ is a prime number. $	herefore \:\:\: a^2 - b^2 = a + b.$

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

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Binomial Theorem

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If aaa and b bb are positive integers such that a2−b2a^2 - b^2a2−b2 is a prime number, then a2−b2a^2 - b^2a2−b2 is