MathDB

Let p(x,y) \equal{} a_0 \plus{} a_1x \plus{} a_2y \plus{} a_3x^2 \plus{} a_4xy \plus{} a_5y^2 \plus{} a_6x^3 \plus{} a_7x^2y \plus{} a_8xy^2 \plus{} a_9y^3. Suppose that \begin{align*}p(0,0) &\equal{} p(1,0) \equal{} p( \minus{} 1,0) \equal{} p(0,1) \equal{} p(0, \minus{} 1) \\&\equal{} p(1,1) \equal{} p(1, \minus{} 1) \equal{} p(2,2) \equal{} 0.\end{align*} There is a point

\left(\tfrac {a}{c},\tfrac {b}{c}\right)

for which p\left(\tfrac {a}{c},\tfrac {b}{c}\right) \equal{} 0 for all such polynomials, where

a

b

, and

c

are positive integers,

a

and

c

are relatively prime, and

c > 1

. Find a \plus{} b \plus{} c.

13

Problems(2)