This note considers the problem of determining, for fixed k and m, all values of r, 0 [less than] r [less than] [empty set](m), such that k[superscript [empty set](m)+1] [equivalent to] k[superscript r](mod m). More generally, if k, m and c are given, necessary and sufficient conditions are given for k[superscript c] [equivalent to] k[superscript r](mod m), 0 [less than or equal to] r [less than] c.