Date of Award


Document Type


Degree Name

Master of Science (MS)


Mathematical Sciences

Committee Member

Kevin James, Committee Chair

Committee Member

Hui Xue

Committee Member

Felice Manganiello


We study the number of ways in which n ≥ 0 be written as the sum of powers of m ≥ 2. After briefly discussing historical results and examples, we prove recurrence relations, exact formulae, bounds, and asymptotic formulae. The proofs are based on elementary reasoning using induction and the mean value theorem.



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