Just for fun!-XI

Algebra Level 3

Let \(F(x)\) be a unique polynomial of degree \(4\) such as \(F(165)=20\)

\(F(42)=F(69)=F(96)=F(123)=13\)

Compute \(F(1)-F(2)+F(3)-F(4)+...+F(165)\)

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