How many pairs of perfect squares between 1 and 100 inclusive differ by a prime number?
Well!. List all the perfect squares and, by trial and error, find out by subtracting one from the others.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Try from the last and go backwards like this:
100 - 81 = 19, which is a prime
100 - 64 = 36, which is NOT prime.
100 - 49 = 51, which is NOT prime......and so on until you reach 1. Then try the next to the last number, or 81 and continue until you finish them all. Then count the pairs that differ by a prime number.And that is it!.
