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pairs with q < 2are equally numbered as those with q > 2, if q = b/a

Source: 1986 Swedish Mathematical Competition p3

March 28, 2021
algebrarational

Problem Statement

Let N≥3N \ge 3 be a positive integer. For every pair (a,b)(a,b) of integers with 1≤a<b≤N1 \le a <b \le N consider the quotient q=b/aq = b/a. Show that the pairs with q<2q < 2 are equally numbered as those with q>2q > 2.
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