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If x,y,z, w in R satisfy the following ...

If `x,y,z, w in R` satisfy the following system of equations `x + y +z+w=1,x +2y + 4z +8 w=16, x+3y +9z+27 w = 81 and x +4 y +162 +64 w = 256`, then the pairs which has HCF as 2 is

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