The number 4 has the property that when it is divided by $q^{2}$, the remainder is less than $q^{q^{2}} / 2$, regardless of the value of $q$. List all numbers that have this property.

#
Let's first prove that if $n$ is a natural number, different from 1 and 4, then $n<[\sqrt{2 n}]^{2}$. Indeed, for numbers let $n$ be a natural number, different from 1 and 4. Let $q=[\sqrt{2 n}]$. Then $n<q^{2}$, so the remainder from the division

## Answer

1 and 4.