Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem C. 1350. (April 2016)

C. 1350. Define the sequence $\displaystyle (a_n)$ as follows: $\displaystyle a_1=1$, and $\displaystyle a_{n+1}=a_n+4n$ for $\displaystyle n>0$. Prove that each term of sequence $\displaystyle (a_n)$ can be expressed as a sum of two consecutive square numbers.

(5 pont)

Deadline expired on May 10, 2016.

### Statistics:

 92 students sent a solution. 5 points: 66 students. 4 points: 11 students. 3 points: 4 students. 2 points: 5 students. 1 point: 5 students. 0 point: 1 student.

Problems in Mathematics of KöMaL, April 2016