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Euler's Squares

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

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Diophantine N-tuples

Can you explain why a sequence of operations always gives you perfect squares?

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There's a Limit

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?

Really Mr. Bond

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?