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

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Problem A. 437. (November 2007)

A. 437. Let p>3 be a prime and

$1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{p} = \frac{a}{b}.$

Prove that p⁴ divides ap-b.

(5 pont)

Deadline expired on December 17, 2007.

Statistics:

11 students sent a solution.

5 points: Huszár Kristóf, Korándi Dániel, Kornis Kristóf, Lovász László Miklós, Nagy 235 János, Nagy 314 Dániel, Tomon István, Tossenberger Anna, Tuan Nhat Le, Wolosz János.

3 points: 1 student.

Problems in Mathematics of KöMaL, November 2007

11 students sent a solution.
5 points:	Huszár Kristóf, Korándi Dániel, Kornis Kristóf, Lovász László Miklós, Nagy 235 János, Nagy 314 Dániel, Tomon István, Tossenberger Anna, Tuan Nhat Le, Wolosz János.
3 points:	1 student.