examday

/TMUA

A positive integer is called balanced if and only if it can be written as the sum of two or more consecutive positive integers. For example, $9$ is balanced since $9=4+5$, and $15$ is balanced since $15=7+8$.

A (true) theorem states that:

A positive integer is balanced if and only if it is not a power of $2$.

So $1,2,4,8,16,\ldots$ are precisely the positive integers that are not balanced.

Which one of the following statements is not true?