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Does there Exist an Algorithm which to Each Diophantine Equation Assigns an Integer which is Greater than the Modulus of Integer Solutions, if these Solutions form a Finite Set?
Let En = {xi = 1; xi + xj = xk ; xi · xj = xk : i; j; k ∈ {1,...,n}}. We conjecture that if a system $S \subseteq E_n$ has only finitely many solutions in integers x1 ,...,xn , then each such solution (x1 ,...,xn ) satisfies …