MathDB
A 99

Source:

May 25, 2007
Divisibility Theory

Problem Statement

Let n≥2n \ge 2 be a positive integer, with divisors 1=d1<d2<⋯<dk=n  .1=d_{1}< d_{2}< \cdots < d_{k}=n \;. Prove that d1d2+d2d3+⋯+dk−1dkd_{1}d_{2}+d_{2}d_{3}+\cdots+d_{k-1}d_{k} is always less than n2n^{2}, and determine when it divides n2n^{2}.
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