Find the remainder of the Euclidean division of $x^{100}-2 x^{51}+1$ by $x^{2}-1$.

 untranslated text:
Trouver le reste de la division euclidienne de $x^{100}-2 x^{51}+1$ par $x^{2}-1$.
Let $P(x)=x^{100}-2 x^{51}+1$. We write the Euclidean division of $P$ by $x^{2}-1:$

$$
P(x)=Q(x)\left(x^{2}-1\right)+R(x)
$$

with $R$ a polynomial of degree less than or equal to 1, that is, of the form $R(x)=a x+b$. We have $R(1)=P(1), R(-1)=P(-1)$, which allows us to calculate $R(X)=-2 X+2$.