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Australian Intermediate Mathematics Olympiad 2015 Question 4

AIMO AUSTRALIA · Australian Intermediate Mathematics Olympiad 2015

Question 4

A fraction, expressed in its lowest terms $\frac ab$, can also be written in the form $\frac2n+\frac1{n^2}$, where $n$ is a positive integer. If $a+b=1024$, what is the value of $a$?

Numerical answer only; a non-negative integer less than 1000.