AoPS Wiki talk:Problem of the Day/July 16, 2011
Problem
AoPSWiki:Problem of the Day/July 16, 2011
Solution
Note that
.
Then, using the Sophie Germain Identity, we have:
.
The discriminant of these quadratics are and
which are both less than
.
Therefore, these quadratics cannot be factored into real linear factors, and the irreducible factorization is