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ambr integers B squared minus a squared equal to a we want to find a and b in first step we lets write main equation B squared minus a squared equal to a in next step we take well lets say we add a square to both sides or we can take we can say we take negative a square to the right hand side so we have B squared equal to a squared plus a and then on right hand side we factor from a it will be a times a plus one now whats my what can we conclude from here it is a perfect square and it is product of two consecutive numbers A and A plus one their gcd is what means their common factor greatest common divisor is one they are relatively prime a and a plus one means dont have any common factors so if two numbers product of two numbers like a A plus one equal to a perfect square and they are relatively prime or they dont have any common factor we can conclude each of them should be perfect square so lets write we can save a has to be a perfect square like x squared and a plus one also