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?
Good solutions here came from Sam, Dave,
Richard and Joe, Matthew and Ross, all at Madras College, St
Andrews. Other people tested special cases but did not prove the