On a Conjecture Involving Fermat's Little Theorem Clark, John Using Fermat's Little Theorem, it can be shown that the sum i raised to m-1, for i from 1 to m, is congruent to -1 modulo m if m is prime. It has been conjectured that the converse is true as well. Namely, that the sum i raised to m-1, for i from 1 to m, is congruent to -1 modulo 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 less than or equal to one trillion. English
On a Conjecture Involving Fermat's Little Theorem
Clark, John
Using Fermat's Little Theorem, it can be shown that the sum i raised to m-1, for i from 1 to m, is congruent to -1 modulo m if m is prime. It has been conjectured that the converse is true as well. Namely, that the sum i raised to m-1, for i from 1 to m, is congruent to -1 modulo 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 less than or equal to one trillion.
English