Question 21
Let $m(x)$ be the unique monic polynomial (leading coefficient $1$) of degree $67$ with rational coefficients such that
$$\frac{1+67^{1/67}+67^{2/67}+\cdots+67^{66/67}}{66}$$
is one of its roots. Let $A$ denote the coefficient of $x^2$ in $m(x)$. Find the value of $|\lfloor A\rfloor|$.
$$\frac{1+67^{1/67}+67^{2/67}+\cdots+67^{66/67}}{66}$$
is one of its roots. Let $A$ denote the coefficient of $x^2$ in $m(x)$. Find the value of $|\lfloor A\rfloor|$.