Finding A Large Reducible Polynomial

Algebra Level 5

Find the largest integer N<1000N<1000 such that the polynomial fN(x)=x6+x5+x4+Nx3+x2+x+1f_N(x)=x^6+x^5+x^4+Nx^3+x^2+x+1 is reducible over the integers.

Definition: A polynomial that is reducible over the integers can be expressed as a product of two non-constant polynomials with integer coefficients.

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