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Problem of the Week 1139

The Mysterious 17th Divisor

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Suppose a positive integer n has divisors d(i), where

1 = d(1) < d(2) < d(3) < . . . < d(k) = n

and

d(7)² + d(15)² = d(16)².

What are the possible values of d(17)?

Source: Feb. 2010 Crux Mathematicorum p. 27; from 2006 Indian Olympiad Team Selection.

© Copyright 2010 Stan Wagon. Reproduced with permission.

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30 November 2010