Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem A. 418. (January 2007)

A. 418. Show that for all pair of reals 0<a<b there exists a positive integer n such that

$a < \frac{\varphi(n+2)}{\varphi(n)} < b.$

(Italian problem)

(5 pont)

Deadline expired on February 15, 2007.

5 students sent a solution.

5 points: Nagy 224 Csaba, Tomon István.

4 points: Nagy 235 János.

1 point: 2 students.