On page 6 in Barbeau's Polynomials, the following problem is given:
I attempted to prove it by induction with the base case as $k = 1$. It is trivially true since $1+t = 1+t$ for all $t$. But if we take $k = 2$, the equation asserts that $1 + t + t^2 + t^3 = 1+ t+t^2$ which is not true for all $t$.
Am I correct that there is something wrong, or am I making some mistake in understanding the problem?