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Satisfy equation bc - ad = 1

Source: IMO LongList 1988, USS 4, Problem 87 of ILL

November 9, 2005
algebra unsolvedalgebra

Problem Statement

In a row written in increasing order all the irreducible positive rational numbers, such that the product of the numerator and the denominator is less than 1988. Prove that any two adjacent fractions ab\frac{a}{b} and cd,\frac{c}{d}, ab<cd,\frac{a}{b} < \frac{c}{d}, satisfy the equation b⋅c−a⋅d=1.b \cdot c - a \cdot d = 1.
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