We use $\bigtriangleup _i$ to denote either multiplication or addition.
Suppose we have a polynomial $P(x,y,z)$ over some algebraic closed field such that:
There are $Q(x), W_1(x,y),W_2(x,z)$ sucht that $P(x,y,z)=Q(W_1(x,y)\bigtriangleup _1W_2(y,z)) $
There are $T(x), R_1(x,y),R_2(x,z)$ such that $P(x,y,z)=T(R_1(x,z)\bigtriangleup _2R_2(y,z)) $
- There are $V(x), K_1(x,y),K_2(x,z)$ such that $P(x,y,z)=V(K_1(x,z)\bigtriangleup _3K_2(y,x)) $
Is it true that there must be $L(x),B_1(x),B_2(x),B_3(x)$ such that: $P(x,y,z)=L(B_1(x)\bigtriangleup _4B_2(y)\bigtriangleup _5B_3(z)) $?
