JP Journal of Algebra, Number Theory and Applications
Volume 23, Issue 1, Pages 25 - 59
(November 2011)
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ON SUMS OF THREE SQUARES AND COMPOSITIONS INTO SQUARES AND TRIANGULAR NUMBERS
AgustÃn Moreno Cañadas and MarÃa Alejandra Osorio Angarita
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Abstract: We use some recent results concerning universal mixed sums of squares and triangular numbers in order to prove that all positive integers n of the form can be written as a sum of three squares of numbers of a given shape. We also use some -partitions in order to obtain formulas for the number of some restricted compositions of a positive integer n in which any partial sum of the parts is a given mixed sum of squares and triangular numbers. |
Keywords and phrases: composition, Diophantine equation, partition,
-partition, quadratic form, representation, square number, triangular number. |
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