The Diophantine Problem for Addition and Divisibility
نویسنده
چکیده
An algorithm is given for deciding existential formulas involving addition and the divisibility relation over the natural numbers. In this paper it will be shown that there is an algorithm for deciding formulas of the form k 0) 3x,.3x„6N A /,(*.,..., xn)\g¡(xx, ...,xtt) /-I in N (the natural numbers), where the / and g¡ are linear polynomials with integer coefficients. (a\b means "a divides b".) This is a generalization of the Chinese Remainder Theorem (C.R.T.) which states that
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