I need some help, (or advise) how I can solve this problem and in which category I need to put it. The problem state: Let m be a solution of the equation $ y^{2015}-15 y+ 14=0$. Find all possible values for $1+m+m^2+ …+m^{(2015-1)}$.
I can easy see that $m=1 $ is solution of such equation, and m is also a solution by definition. I’m thinking in the superposition principle due to be a sum of all the possible solution is also a solution. But I am not sure how it is possible find all possible values.
Thanks .
Notice that $m\neq 0$ and rewrite the condition as $m^{2015}=15m-14$. You already thought about the case $m=1$.
If $m\neq 1$ $$1+m+\dots + m^{2014}=\frac{m^{2015}-1}{m-1}=\frac{15m-15}{m-1}=15.$$