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?
115 2 = (110 x 120) + 25
that is 13225
895 2 = (890 x 900) + 25
that is 801025
Can you explain what is happening and generalise?