Mathematical and Physical Journal
for High Schools
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# Problem K. 311. (November 2011)

K. 311. The number 772009+772010+772011+772012 is evidently divisible by 7 and 11. Find all prime factors of the number.

(6 pont)

Deadline expired on December 12, 2011.

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

Megoldás. $\displaystyle 77^{2009}+77^{2010}+77^{2011}+77^{2012}=77^{2009}\left( 1+77+77^2 +77^3 \right)=7^{2009}\cdot 11^{2009}\cdot 462540= 7^{2009}\cdot 11^{2009}\cdot 2^2\cdot 3 \cdot 5 \cdot 13 \cdot 593$.

A feladatbeli kifejezés a következő prímszámokkal osztható: 2, 3, 5, 7, 11, 13, 593.

### Statistics:

 183 students sent a solution. 6 points: 107 students. 5 points: 22 students. 4 points: 8 students. 3 points: 10 students. 2 points: 6 students. 1 point: 15 students. 0 point: 12 students. Unfair, not evaluated: 3 solutionss.

Problems in Mathematics of KöMaL, November 2011