Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
Can you explain why a sequence of operations always gives you perfect squares?
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you
notice when successive terms are taken? What happens to the terms
if the fraction goes on indefinitely?
Is it always the case that when you square a number whose last
digit is 5 you always end with 25?
By breaking the number down into a form (x + 5) it may then be
possible to see what is happening and why.