## Problem 4

$A=n \cdot(1+4+7+\ldots+58)(2p)$

$A=n \cdot 590$ (2p)

$A=n \cdot 2 \cdot 5 \cdot 59$ (2p)

$n=2 \cdot 5 \cdot 59=590(1p)$

Note: a) Each corrector awards an integer number of points.

b) Any other correct solution is graded accordingly.

## NATIONAL MATHEMATICS OLYMPIAD

Local stage - 09.02.2013

## 5th Grade
## Problem 4

Determine the smallest natural number $n$, non-zero, for which the number $A=n \cdot 1+n \cdot 4+n \cdot 7+\ldots+n \cdot 58$ is a perfect square.

Problems selected by Prof. Petruța Gelu

Note: a) The actual working time is 3 hours.

b) All problems are mandatory.

c) Each problem is scored from 0 to 7.