Question 3
A positive integer $n \ge 2$ is lucky if $n^2$ can be represented as a sum of $n$ consecutive positive integers. Prove that:
a) the number $7$ is lucky,
b) the number $10$ is not lucky,
c) the product of any two lucky numbers is a lucky number.
a) the number $7$ is lucky,
b) the number $10$ is not lucky,
c) the product of any two lucky numbers is a lucky number.