Jerry W. Lewis wrote...
And I cannot reproduce #2 (even after correcting for formatting problems)
=MOD(987654321098765*8+1,543210987654321)
returns the correct answer, despite a 16-digit first argument.
....

OK, but the main point should be that Excel doesn't use IEEE 64-bit
modulus. In hardware terms, Excel's MOD is (unfortunately) more than
just a simple wrapper around the Wintel FPU's FPREM1 operation.

Yes, that's right folks, Excel screws up some arithmetic operations,
and while it may or may not have been intentional, it may be inferred
from

http://support.microsoft.com/default...b;en-us;119083

that Microsoft has no immediate plans to fix it.

what a company! [In case anyone needs a lesson in why lack of
competition is a BAD THING . . .]