In this paper we study quadratic forms which are universal when restricted to almost prime inputs, establishing finiteness theorems akin to the Conway-Schneeberger 15 theorem.
In this paper we study diagonal quadratic forms which are universal when restricted to almost prime inputs, establishing finiteness theorems akin to the Conway–Schneeberger 15 theorem.
In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain the minimal number of generalized m-gonal numbers required to represent every positive integer and we furthermore generalize this result to obtain optimal bounds when many of the generalized m-gonal numbers are repeated r times, where r ∈ N is fixed.
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