Question

Let $a,b$ are positive integers such that $a^2-b^2=7$ then find $a,b$.

Answer 1

Given for $a,b$ to be positive integers such that

$a^2-b^2=7$

or, $(a+b)(a-b)=7\times 1$

or, $a+b=7$.....(1) and $a-b=1$......(2). [ Since $a,b$ are positive integers]

Now adding (1) and (2) we get,

$2a=8$

or, $a=4$.

Again subtracting (2) from (1) we get,

$2b=6$

or, $b=3$.

So the numbers are $4,3$.