If I submit the expression
simplify((-1)^(2+j-m));
with the assumption j integer and m integer the result is always 1. Does this strike you?
This bug seems to be corrected in Maple 6.
Whow! I verified the "simplification" in Rel. 5.1; Maple 6.01 yields the correct value (-1)^(j-m) however.
Strange enough: (-1)^(2+j-m+n) is computed correctly by Rel. 5.1, (-1)^(2+j-m+n+r) is wrong again. Probably one can generalize the bug to an odd and an even number of assumed variables...