Problem C. 982.

Order KöMaL!

ELTE

Competitions Portal

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

(5 points)

Deadline expired.

Sorry, the solution is published in Hungarian only.

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 on problem C. 982.

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

Our web pages are supported by:

ELTE