# Solution July 21, 2007

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### Problem

What is the largest positive integer such that is divisible by ?

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### Solution

*n* + 10 | *n*^{3} + 100 is equivalent to gcd(*n* + 10,*n*^{3} + 100) = *n* + 10
By the rules for the gcd (*http://en.wikipedia.org/wiki/Greatest_common_divisor*) we have

In other words, *n* + 10 | 900 and the largest such *n*
is *n* = 890.