4. Consider the numbers $A=1+2+3+\ldots+2016^{2}$ and $B=2+4+6+\ldots+2016^{2}$.

a) Find the last digit for each of the numbers $A$ and $B$.

b) Show that $A-B$ is a perfect square.

The problems were proposed by: Prof. Mariana Guzu, School "D. Zamfirescu" Prof. Marius Mohonea, C.N. "Unirea"

NOTE: Working time: 2 hours.

Each problem is graded from 0 to 7 points.

## NATIONAL MATHEMATICS OLYMPIAD

Local stage - 20.02.2016

5th Grade

Grading and marking guide