grandes-ecoles 2019 Q9

grandes-ecoles · France · x-ens-maths1__mp Number Theory Algebraic Number Theory and Minimal Polynomials
We fix an integer $n \geq 2$.
(a) Calculate $\Phi _ { n } ( 0 )$.
(b) Calculate $\Phi _ { n } ( 1 )$ as a function of the prime factorization of $n$. Hint: reason by induction on $n$, using question 7.
We fix an integer $n \geq 2$.\\
(a) Calculate $\Phi _ { n } ( 0 )$.\\
(b) Calculate $\Phi _ { n } ( 1 )$ as a function of the prime factorization of $n$.\\
Hint: reason by induction on $n$, using question 7.