MathDB
A farmer and his trees

Source: 2009 SDMO Middle School Problem 1

August 24, 2016

Problem Statement

A farmer buys a batch of trees, which he wishes to plant in a square grid. For example, if he had 2525 trees, then he could plant them as shown below.
[asy] size(3cm,0); dot((0,0)); dot((0,1)); dot((0,2)); dot((0,3)); dot((0,4)); dot((1,0)); dot((1,1)); dot((1,2)); dot((1,3)); dot((1,4)); dot((2,0)); dot((2,1)); dot((2,2)); dot((2,3)); dot((2,4)); dot((3,0)); dot((3,1)); dot((3,2)); dot((3,3)); dot((3,4)); dot((4,0)); dot((4,1)); dot((4,2)); dot((4,3)); dot((4,4)); [/asy]
However, the farmer finds that he cannot plant his trees in a square grid. If he had 2020 more trees, or if he had 3939 fewer trees, then he could plant his trees in a square grid. How many trees did the farmer buy?