On a Conjecture about the Number of Solutions to Linear Diophantine Equations with a Positive Integer Parameter
نویسندگان
چکیده
Let A(n) be a k × s matrix and m(n) be a k dimensional vector, where all entries of A(n) and m(n) are integer-valued polynomials in n. Suppose that t(m(n)|A(n)) = #{x ∈ Z + | A(n)x = m(n)} is finite for each n ∈ N, where Z+ is the set of nonnegative integers. This paper conjectures that t(m(n)|A(n)) is an integer-valued quasi-polynomial in n for n sufficiently large and verifies the conjecture in several cases. 2000 AMS Classification: Primary 05A15, Secondary 11D45, 11P99
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تاریخ انتشار 2008