The unboundedness of a family of difference equations over the integers

John Greene

The unboundedness of a family of difference equations over the integers

John Greene

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we prove that positive integer solutions {a_n to an = {c₁-1+c₂-2+...+c_k-k/d, c ₁-1+c₂-2+...+c_k-k if d!c₁-1+c ₂-2+...+c_ka_n-ki otherwise, where the c's are nonnegative integers, and d=c₁-1+c₂-2+...+c_k, have the property that either {a_n} is periodic with period at most k, or {a_n} is unbounded.

Original language	English (US)
Pages (from-to)	146-152
Number of pages	7
Journal	Fibonacci Quarterly
Volume	46-47
Issue number	2
State	Published - Dec 1 2008

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title = "The unboundedness of a family of difference equations over the integers",

abstract = "In this paper, we prove that positive integer solutions \{an to an = \{c1-1+c2-2+...+ck-k/d, c 1-1+c2-2+...+ck-k if d!c1-1+c 2-2+...+ckan-ki otherwise, where the c's are nonnegative integers, and d=c1-1+c2-2+...+ck, have the property that either \{an\} is periodic with period at most k, or \{an\} is unbounded.",

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AB - In this paper, we prove that positive integer solutions {an to an = {c1-1+c2-2+...+ck-k/d, c 1-1+c2-2+...+ck-k if d!c1-1+c 2-2+...+ckan-ki otherwise, where the c's are nonnegative integers, and d=c1-1+c2-2+...+ck, have the property that either {an} is periodic with period at most k, or {an} is unbounded.

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The unboundedness of a family of difference equations over the integers

Abstract

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