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11st ibmo - costa rica 1996/q4.

Source: Spanish Communities

April 23, 2006
inductionnumber theory unsolvednumber theory

Problem Statement

Given a natural number n≥2n \geq 2, consider all the fractions of the form 1ab\frac{1}{ab}, where aa and bb are natural numbers, relative primes and such that: a<b≤na < b \leq n, a+b>na+b>n. Show that for each nn, the sum of all this fractions are 12\frac12.
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