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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

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.