11

Part of 2000 Harvard-MIT Mathematics Tournament

Problems(2)

2000 Guts #11: Maximum value

Source:

M

be the maximum possible value of

x_1x_2+x_2x_3+\cdots +x_5x_1

x_1, x_2, \cdots x_5

is a permutation of

(1,2,3,4,5)

N

be the number of permutations for which this maximum is attained. Evaluate

M+N

2000 HMMT RMT Team #11

Source:

Find all polynomials

f(x)

with integer coefficients such that the coefficients of both

f(x)

[f(x)]^3

\{0,1, -1\}