Question 114
Determine all pairs $(a,b)$ of positive integers satisfying these three conditions:
- $b\gt a$ and $b-a$ is prime;
- the units digit of $a+b$ is $3$;
- $ab$ is the square of an integer.
- $b\gt a$ and $b-a$ is prime;
- the units digit of $a+b$ is $3$;
- $ab$ is the square of an integer.