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.


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