Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 436. (October 2007)

A. 436. Prove that

for every positive integer n.

(5 pont)

Deadline expired on November 15, 2007.

Solution. Let and . Then , since is irrational.

Write

The numerator is an integer which is not 0. In the denominator we have

and

therefore

We obtained that

### Statistics:

 7 students sent a solution. 5 points: Korándi Dániel, Lovász László Miklós, Nagy 235 János, Tomon István. 3 points: 1 student. 1 point: 1 student. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, October 2007