Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem C. 1006. (November 2009)

C. 1006. Prove that six-digit numbers of the form cannot have prime factors of more than two digits.

(5 pont)

Deadline expired on December 10, 2009.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. $\displaystyle \overline{ababab}=10101(10a+b)=3 \cdot 7 \cdot 13 \cdot 37 \cdot \overline{ab}$. Mivel $\displaystyle \overline{ab}$ kétjegyű, ezért legfeljebb kétjegyű prímosztója lehet csak.

### Statistics:

 367 students sent a solution. 5 points: 281 students. 4 points: 47 students. 3 points: 14 students. 2 points: 16 students. 1 point: 1 student. 0 point: 3 students. Unfair, not evaluated: 5 solutions.

Problems in Mathematics of KöMaL, November 2009