Request for "Decimal Period of 1/X in Base Y" program

[Gerald H]

(02-27-2015 06:13 AM)Joe Horn Wrote:  Has anybody already written a Prime program to calculate the Number Theory value of "the multiplicative order of Y (mod X)"?

One application of this concept is found in repeating decimal numbers. For example, 1/13 = 0.076923076923... where "076923" repeats forever. Notice that the repeating section of 1/13 is 6 digits long. In Number Theory, they express this as "the multiplicative order of 10 (mod 13) = 6" with the 10 coming from the fact that decimal numbers (as the name implies) use base 10. "Multiplicative order" is often shortened to just "order".

Another example: In hexadecimal, 1/Dh (that's 1/13 in decimal) = 0.13B13B13B...h, where the three hex digits "13B" repeat forever. So the order of 16 (mod 13) = 3.

In Mathematica, it's implemented as MultiplicativeOrder[y,x].

Thanks in advance to anybody who has already programmed their Prime to find the order of Y (mod X). It shouldn't be too hard, since Prime has EULER, IDIVIS, and MODPOW built in.

Are you only interested in integer values of X & Y?