rectangle ABCD, point E is on AB and point F is on AD. Angle
CEF is a right angle. Draw triangle CEF.
The rectangle is divided into four triangles (AEF, BEC, DCF,
three sides of each triangle are integers, and CF is the longest line
diagram. What is the smallest possible length of CF?
Extension: What solutions
exist for CF < 100? In particular what solutions exist which
aren't multiples of smaller solutions? ource: Original.