Problem #5

Paul Erdös died Friday, September 20, in Warsaw, Poland at the age of 83. One of the many (as yet unsolved) problems he studied was the maximal size of a subset {a_1,...,a_k} of {1,2,...,n} such that a_i + a_j is never a perfect square. For example, if n=7 then {1,4,6,7} is an example of such a subset. [Note that 2 can never be in such a set since 2+2=4.]

In honor of Erdös, this week's challenge is to find a maximal subset of {1,2,...,100} having this property.

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