A Prime Problem

Given that a and b are positive integers and that:Find the possible value(s) of a and b.

Ans

This problem can be given after students have learnt to factorize to challenge them. By now, they will be thinking... Huh? Only one equation, how to solve for 2 unknowns?

But lets try to factorize first. We will get:

(a + b) (a - b) = 97

What students have to realize here to proceed is to recognize that 97 is a prime number.

Hence, a + b = 97 and a - b = 1

Solving those 2 equations give us a = 49 and b = 48

This question can of course be reduced to smaller primes to simplify this problem or even non-primes but that will give multiple pairs of solutions. If I had not stated that a and b must be positive integers, students must also consider for the possibility that a + b = 1 and that a - b = 97 for the negative solutions.