MathDB

87

Part of 1988 IMO Longlists

Problems(1)

Satisfy equation bc - ad = 1

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

11/9/2005
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.
algebra unsolvedalgebra