MathDB

Suppose that

P(x, y, z)

is a homogeneous degree 4 polynomial in three variables such that

P(a, b, c) = P(b, c, a)

and

P(a, a, b) = 0

for all real

a

b

, and

c

. If

P(1, 2, 3) = 1

, compute

P(2, 4, 8)

.
Note:

P(x, y, z)

is a homogeneous degree

4

polynomial if it satisfies

P(ka, kb, kc) = k^4P(a, b, c)

for all real

k, a, b, c

Problem Statement