I want to find the value of h0,h1,h2,h3,h4 such that (x -
a1)*(x-a2)*(x-a3)*(h0+h1*x^1+h2*x^2+h3*x^3+h4*x^4+x^5)=(x+b)*g2+(a*x+d) for
some a,b,d,in GF(p). Below is my code which is unable to solve it
a,b,d,a1,a2,a3,h0,h1,h2,h3,h4=var('a b d a1 a2 a3 h0 h1 h2 h3 h4')
RHS= (x - a1)*(x-a2)*(x-a3)*(h0+h1*x^1+h2*x^2+h3*x^3+h4*x^4+x^5)
g2=x^7 + 74604*x^6 + 351974*x^5 + 18952*x^4 + 148817*x^3 + 256076*x^2 +
168356*x +278165
LHS=(x+b)*g2+(a*x+d)
Coeff = RHS.coefficients(x,sparse=False)
print(solve(RHS==LHS, h0,h1,h2,h3,h4))
Please provide me suggestions
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