What is the correct formula for the compound made by magnesium and nitrogen?

Magnesium and nitrogen combine to form magnesium nitride, ##"Mg"_3"N"_2"##.

Magnesium nitride is an ionic compound. Magnesium forms ions with a ##"2+"## charge, and nitrogen forms nitride ions with a ##"3-"## charge. The overall charge of the compound must be zero. Therefore, the numerical value of the positive and negative charge must be ##"6"##.

##3["Mg"]^(2+) + 2 ["N"]^(3-)####rarr####"Mg"_3"N"_2"##

##3xx(2+)=6+## and ##2xx(3-)=6-##

##(6+)+(6-)=0##

An easy way to determine the formula unit of an ionic compound is called the crisscross method, as demonstrated in the video below.