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Suppose that the polynomial x^2+y^2-1 is not irreducible.
It means that there exists two fractions such that :
We found that q divide t and q divide s, but s and t are supposed to be prime each other. It is a contradiction.
The polynomial x^2+y^2-1 is then irreducible in q[x,y]
It means that there exists two fractions such that :
We found that q divide t and q divide s, but s and t are supposed to be prime each other. It is a contradiction.
The polynomial x^2+y^2-1 is then irreducible in q[x,y]
