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Dutch Mathematical Olympiad

Netherlands number theory

Problem

How many pairs of positive integers

a

and

b

with

a < b

are there such that

\frac{1}{a} + \frac{1}{b} = \frac{4}{15} ?

A) 1 B) 2 C) 3 D) 4 E) 5

Solution

C) 3

Final answer

Techniques

Techniques: modulo, size analysis, order analysis, inequalitiesSimple Equations