3

Part of 1986 Swedish Mathematical Competition

Problems(1)

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

Source: 1986 Swedish Mathematical Competition p3

N \ge 3

be a positive integer. For every pair

(a,b)

of integers with

1 \le a <b \le N

consider the quotient

q = b/a

. Show that the pairs with

q < 2

are equally numbered as those with

q > 2

algebrarational