TIGHT UNIVERSAL SUMS OF m -GONAL NUMBERS.

For a positive integer n , let $\mathcal T(n)$ denote the set of all integers greater than or equal to n. A sum of generalised m -gonal numbers g is called tight $\mathcal T(n)$ -universal if the set of all nonzero integers represented by g is equal to $\mathcal T(n)$. We prove the existence of a minimal tight $\mathcal T(n)$ -universality criterion set for a sum of generalised m -gonal numbers for any pair $(m,n)$. To achieve this, we introduce an algorithm giving all candidates for tight $\mathcal T(n)$ -universal sums of generalised m -gonal numbers. Furthermore, we provide some experimental results on the classification of tight $\mathcal T(n)$ -universal sums of generalised m -gonal numbers. [ABSTRACT FROM AUTHOR]