Mathematical and Physical Journal
for High Schools
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Problem C. 1006. (November 2009)

C. 1006. Prove that six-digit numbers of the form \overline{ababab} 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.


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