It is known that k and n are positive integers and k \plus{} 1\leq\sqrt {\frac {n \plus{} 1}{\ln(n \plus{} 1)}}. Prove that there exists a polynomial P(x) of degree n with coefficients in the set \{0,1, \minus{} 1\} such that (x \minus{} 1)^{k} divides P(x). algebrapolynomiallogarithmsalgebra proposed