Degree Granting Department
Mathematics and Statistics
Stephen Suen, Ph.D.
Mohamed Elhamdadi, Ph.D.
Arthur Danielyan, Ph.D.
Number Theory, Prime Numbers, Divisibility, Congruences, Sums of Powers of Consecutive Integers
Using Fermat’s Little Theorem, it can be shown that Σmi=1 i m−1 ≡ −1 (mod m) if m is prime. It has been conjectured that the converse is true as well. Namely, that Σmi=1 i m−1 ≡ −1 (mod m) only if m is prime. We shall present some necessary and sufficient conditions for the conjecture to hold, and we will demonstrate that no counterexample exists for m ≤ 1012 .
Scholar Commons Citation
Clark, John, "On a conjecture involving Fermat's Little Theorem" (2008). Graduate Theses and Dissertations.