At 03:43 PM 6/7/2007, Schroeppel, Richard wrote:

I don't know the history: I don't think the extended notations are used in Hardy & Wright, except maybe for (mod 1) to mean fractional part, or for stuff with algebraic integers.

Actually Hardy & Wright do use this notation, and in exactly the same context as the Monthly article that Dan cited. Theorem 116 says "If p>3, and 1/i is the associate of i (mod p^2), then 1 + 1/2 + 1/3 + ... + 1/(p-1) == 0 (mod p^2)." (By "associate" they mean "multiplicative inverse".) -- Fred W. Helenius fredh@ix.netcom.com