Polynomials

Algebra Level 4

If polynomials \(u,v\in \mathbb{Z}[x]\) such that

\[(x^4-1)u(x)+(x^7-1)v(x)=x-1\]

Find \(u(-1)+v(-1)\).

Details

The set of polynomails with integer coefficients is defined as \(\mathbb{Z}[x]\), for example \(x^3-2x^2+1\in \mathbb{Z}[x]\).

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