Mathematical and Physical Journal
for High Schools
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Problem C. 982. (March 2009)

C. 982. Prove that 52008+4 is a composite number.

(5 pont)

Deadline expired on April 15, 2009.


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

Megoldás.

5^{2008}+4=\left(5^{1004}\right)^2+2^2=
\left(5^{1004}+2\right)^2-5^{1004}\cdot2^2=

=\left(5^{1004}+2\right)^2-\left(5^{502}\cdot2\right)^2=

=\left(5^{1004}+2+2\cdot5^{502}\right)\left(5^{1004}+2-2\cdot5^{502}\right).

Mindkét tényező 1-nél nagyobb, ezzel beláttuk az állítást.


Statistics:

117 students sent a solution.
5 points:98 students.
3 points:1 student.
2 points:4 students.
1 point:4 students.
0 point:8 students.
Unfair, not evaluated:2 solutions.

Problems in Mathematics of KöMaL, March 2009