Stage: 4 Challenge Level: 
Consider numbers of the form $u_n = 1! + 2! + 3! +...+n!$. How many such numbers are perfect squares?
Long problems. Divisibility. Factors and multiples. Sequences. Working systematically. Index notation/Indices. Number - generally. Mathematical reasoning & proof. Modulus arithmetic. Mathematical induction.
Published March 2002.
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