Global resource of innovative mathematical ideas. Discovery for the 21st century. Abstract reductionism realized. And modular rules.
Translate
Tuesday, December 27, 2022
Math is better for comfort
Friday, December 02, 2022
Reassurance with my math
Finally found myself just playing around with my method for finding a modular inverse and was reassuring. Math is that way. Doing a post to let know am still active and to show it again.
So will calculate modular inverse of 19 mod 1001 which is 7(11)(13).
Let 2m = 1 mod 1001, then F0 = 19(19 + y0) mod 1001. Can pick y0 = 34. Then F0 = 6 mod 1001. That was lucky! Can pick whatever I like.
Picking so that F0 is as small as possible without 19 as a factor but coprime to 1001, and usually regardless have found need to recurse with coefficient of d as new modulus.
6d = (6n - 7)(53) mod 1001
6d = 318n - 371 mod 1001
And 6(167) = 1002 = 1 mod 1001 which is very convenient.
So: d = 53n - 896 mod 1001, so can use n = 1 and then d = -843. So 19-1 = 843 mod 1001.
Those values worked better than I expected, as of course really like easy. But yeah is very reassuring to just do some math and get the correct answer.
My way makes calculating the modular inverse so straightforward.
Am still active on this blog but often just reviewing. Have a lot of research results! Can play around endlessly with them.