## Problem of the Day #364: Divisibility PairsMarch 17, 2012

Posted by Saketh in : potd , trackback

Suppose that Albert writes down all numbers of the form $p^0+q^0, p^1+q^1, p^2+q^2, \ldots$ up to $p^n+q^n$, where $p$ and $q$ are distinct primes. Determine, in terms of $n$, the number of unordered pairs of distinct members of this sequence such that one divides the other.