Algebra · Polynomials · Restricted coefficients · Geometric series bounds · Base 3 representation · Uniqueness
Problem 4, 2014
Determine all polynomials \(R(x)\) whose coefficients all belong to the set \(\{-1, 1\}\) and which satisfy
\[ R(3) = 130 \qquad \text{and} \qquad R(-2) = -45 . \]
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Serbian National Competition (Drzavno takmicenje) 2014, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source