Review question

# Can we find a solution to $(n-3)^3+n^3=(n+3)^3$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9919

## Suggestion

Show that, if $n$ is an integer such that $\begin{equation*} (n-3)^3+n^3=(n+3)^3,\label{eq:1sug}\tag{1} \end{equation*}$

then $n$ is even and $n^2$ is a factor of $54$. Deduce that there is no integer $n$ which satisfies the equation $\eqref{eq:1sug}$.

Show that, if $n$ is an integer such that $\begin{equation*} (n-6)^3+n^3=(n+6)^3,\label{eq:2sug}\tag{2} \end{equation*}$

then $n$ is even. Deduce that there is no integer $n$ which satisfies the equation $\eqref{eq:2sug}$.

Can $n$ be even? Be odd? Would multiplying out the brackets help?