View Single Post 2018-03-06, 14:44   #18
Dr Sardonicus

Feb 2017
Nowhere

3·1,481 Posts Quote:
 Originally Posted by JM Montolio A I think axiomatic definition for M() is enough
Pfui. In this post, I listed 20 primes p less than 200 for which your "definition" of M(p) was ambiguous. They could be any value divisible by the multiplicative order of 2 (mod p), and dividing p-1.

I repost the values here for ease of reference:
Quote:
 For p = 17, the possible values of M(p) are 8 times k for k in [1, 2]. For p = 23, the possible values of M(p) are 11 times k for k in [1, 2]. For p = 41, the possible values of M(p) are 20 times k for k in [1, 2]. For p = 43, the possible values of M(p) are 14 times k for k in [1, 3]. For p = 47, the possible values of M(p) are 23 times k for k in [1, 2]. For p = 71, the possible values of M(p) are 35 times k for k in [1, 2]. For p = 73, the possible values of M(p) are 9 times k for k in [1, 2, 4, 8]. For p = 79, the possible values of M(p) are 39 times k for k in [1, 2]. For p = 89, the possible values of M(p) are 11 times k for k in [1, 2, 4, 8]. For p = 97, the possible values of M(p) are 48 times k for k in [1, 2]. For p = 103, the possible values of M(p) are 51 times k for k in [1, 2]. For p = 109, the possible values of M(p) are 36 times k for k in [1, 3]. For p = 113, the possible values of M(p) are 28 times k for k in [1, 2, 4]. For p = 137, the possible values of M(p) are 68 times k for k in [1, 2]. For p = 151, the possible values of M(p) are 15 times k for k in [1, 2, 5, 10]. For p = 157, the possible values of M(p) are 52 times k for k in [1, 3]. For p = 167, the possible values of M(p) are 83 times k for k in [1, 2]. For p = 191, the possible values of M(p) are 95 times k for k in [1, 2]. For p = 193, the possible values of M(p) are 96 times k for k in [1, 2]. For p = 199, the possible values of M(p) are 99 times k for k in [1, 2].
So far, you have failed to resolve the ambiguity in any of them, let alone explain how this may be done.

I'm not a programmer. But from my limited experience with computer programs, being able to explain the algorithm is easier than -- indeed, a prerequisite for -- writing the program.  