Almost universal ternary sums of polygonal numbers

Almost universal ternary sums of polygonal numbers For a natural number m, generalized m-gonal numbers are those numbers of the form $$p_m(x)=\frac{(m-2)x^2-(m-4)x}{2}$$ p m ( x ) = ( m - 2 ) x 2 - ( m - 4 ) x 2 with $$x\in \mathbb Z$$ x ∈ Z . In this paper we establish conditions on m for which the ternary sum $$p_m(x)+p_m(y)+p_m(z)$$ p m ( x ) + p m ( y ) + p m ( z ) is almost universal. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in Number Theory Springer Journals

Almost universal ternary sums of polygonal numbers

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by SpringerNature
Subject
Mathematics; Number Theory
eISSN
2363-9555
D.O.I.
10.1007/s40993-018-0098-x
Publisher site
See Article on Publisher Site

Abstract

For a natural number m, generalized m-gonal numbers are those numbers of the form $$p_m(x)=\frac{(m-2)x^2-(m-4)x}{2}$$ p m ( x ) = ( m - 2 ) x 2 - ( m - 4 ) x 2 with $$x\in \mathbb Z$$ x ∈ Z . In this paper we establish conditions on m for which the ternary sum $$p_m(x)+p_m(y)+p_m(z)$$ p m ( x ) + p m ( y ) + p m ( z ) is almost universal.

Journal

Research in Number TheorySpringer Journals

Published: Jan 31, 2018

References

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