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Maths Item of the Month

September 2014
Square strings

Each number in the sequence 49, 4489, 444889, 44448889 is a perfect square.
i.e. the first digits are always 4s, the next digits are 8s but always 1 fewer of them, the units digit is always 9.

Prove that the numbers are always perfect squares.

Can you find another sequence (of the form XXXXYYZ like above but different digits) that behaves in the same way?

Maths item of the month archive