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Between a Square and a Cube

Stage: 3 Short Challenge Level: Challenge Level:1

x=5

This is the only solution of the equation for which x and y are whole numbers. Another way of looking at this is to say that 26 is the only whole number "sandwiched" between a perfect square and a perfect cube. This was proved by the French mathematician, Pierre de Fermat, in the 17th Century.

 

This problem is taken from the UKMT Mathematical Challenges.