🚀 go-pugleaf

On Tue, 18 Jan 1994, george tintera wrote:
[...]
> afternoon and started getting wrong moduli.  specifically...
> mod(2**47,47)  returns the value 4 rather than the correct value of 2.
>       (yes, on my calculator i used a 'caret' rather than **).
>
George, the problem here is not with "mod" per se.  2^47 is about 1.4E14,
and is larger than the TI-85 can calculate exactly (The TI-85 carries 14
digits internally, but displays fewer).  Thus, 2^47, having 15 digits, is
stored in the machine without the crucial "ones place".

Who knows WHAT the mod does with numbers whose digits are not known down
to the decimal point.

More relevant, I've got a bunch of number theory programs for the TI-85
that will do what you want, including modular powers of numbers up to 2E13,
for powers up to about the same, provided the modulus is <= about 2E13.

The trick is to take the modular residue after each multiplication.  This
is much faster than it sounds, though, since you square your base repeatedly
and use the results to quickly build the desired power.

Anyway, give me a day or two and I'll send you some programs.  Please
let me know by private mail if you've got a TI-link or if you need ASCII code.
Regards,

Mark Janeba			(503)370-6123
Dept. of Mathematics		e-mail:  mjaneba@willamette.edu
Willamette University		"Speaking for myself, not the university"
Salem, Oregon 97301-3922 USA