(1-x)(1-x^2)... [particular case of pentagonal number thm.]
Source: Chinese TST 2007 4th quiz P2
March 26, 2007
algebrapolynomialEulernumber theory unsolvednumber theory
Problem Statement
After multiplying out and simplifying polynomial (x \minus{} 1)(x^2 \minus{} 1)(x^3 \minus{} 1)\cdots(x^{2007} \minus{} 1), getting rid of all terms whose powers are greater than we acquire a new polynomial Find its degree and the coefficient of the term having the highest power. Find the degree of f(x) \equal{} (1 \minus{} x)(1 \minus{} x^{2})...(1 \minus{} x^{2007})