Question 25
Let p(x)=x⁶+x⁵+x⁴+x³+x²+x+1 and “six numbers” a₀, a₁,…, a₆ satisfy p(x)=a₆(x−1)⁶+a₅(x−1)⁵+a₄(x−1)⁴+a₃(x−1)³+a₂(x−1)²+a₁(x−1)+a₀. What is a₀+a₁+a₂+a₃+a₄+a₅+a₆?
Editorial note: The source says six numbers but lists seven coefficients, a₀ through a₆; retain all seven in the displayed identity and sum.
Editorial note: The source says six numbers but lists seven coefficients, a₀ through a₆; retain all seven in the displayed identity and sum.