Let
![P(x)](/media/m/c/d/7/cd7664875343d44cd5f96a566b582b0e.png)
be a polynomial with integer coefficients. We denote
![\deg(P)](/media/m/e/7/4/e7487f007a0d3fba50ac4d4523d5ed70.png)
its degree which is
![\geq 1.](/media/m/d/6/4/d64a7d999d9feac0b2804178aeb213d9.png)
Let
![n(P)](/media/m/f/3/3/f337f6d49d90dec5cd873dd6f9ecf2c9.png)
be the number of all the integers
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
for which we have
![(P(k))^{2}=1.](/media/m/2/5/2/252edb118fe20a1f95106e1c57683991.png)
Prove that
%V0
Let $P(x)$ be a polynomial with integer coefficients. We denote $\deg(P)$ its degree which is $\geq 1.$ Let $n(P)$ be the number of all the integers $k$ for which we have $(P(k))^{2}=1.$ Prove that $n(P)- \deg(P) \leq 2.$