Some conjectures on addition and multiplication of complex (real) numbers
Abstract
We discuss conjectures related to the following two conjectures: (1) for each complex numbers x1,...,xn there exist rationals y1,...,yn ∈ [-2n-1,2n-1] such that ∀ i ∈ 1,...,n (xi=1 ⇒ yi=1) ∀ i,j,k ∈ 1,...,n (xi+xj=xk ⇒ yi+yj=yk) (2) for each complex (real) numbers x1,...,xn there exist complex (real) numbers y1,...,yn such that ∀ i ∈ 1,...,n |yi| ≤ 22n-2 ∀ i ∈ 1,...,n (xi=1 ⇒ yi=1) ∀ i,j,k ∈ 1,...,n (xi+xj=xk ⇒ yi+yj=yk) ∀ i,j,k ∈ 1,...,n (xi · xj=xk ⇒ yi · yj=yk)
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