I had an opportunity to work with Dr. Beauregard Stubblefield 35 years ago (yep, 62 and proud of it) and he generously gave the credit for the group's result to Dr. Mary Buxton and me. Dr. Stubblefield of course did most of the work, and he and I discussed many things. It seems that Leopold Kronecker, the great German algebraist 1823-1891, had it right the whole time. He proved that X = p^e + p^(e+1) + ... + p^2 + p + 1, where e is one less than a prime and p is a prime, cannot be algebraically reduced. But we knew that. The big deal is that the numeric factors of the expression are either (e + 1) || X or (k(e + 1) + 1) | X. Dr. Stubblefield found the pattern and I found that Kronecker had proved it. Stubblefield used the result in his Proposition 11, which he proved. Thirty-five years ago we used the result to factor many sigma(p^e). We talked about extending the result back then so we both had deep input into the new theory. Recently, after an engineering career in the auto industry in Detroit, I extended Proposition 11 to apply to many more cases in several different ways. I think, Cam, that this is the road you are suggesting. Steve Elmorestevelmore@gmail.com
|
2 | Removed email address, added full name. | ||
|
|
||||
|
|
1 |
|
||
|
I had an opportunity to work with Dr. Beauregard Stubblefield 35 years ago (yep, 62 and proud of it) and he generously gave the credit for the group's result to Dr. Mary Buxton and me. Dr. Stubblefield of course did most of the work, and he and I discussed many things. It seems that Leopold Kronecker, the great German algebraist 1823-1891, had it right the whole time. He proved that X = p^e + p^(e+1) + ... + p^2 + p + 1, where e is one less than a prime and p is a prime, cannot be algebraically reduced. But we knew that. The big deal is that the numeric factors of the expression are either (e + 1) || X or (k(e + 1) + 1) | X. Dr. Stubblefield found the pattern and I found that Kronecker had proved it. Stubblefield used the result in his Proposition 11, which he proved. Thirty-five years ago we used the result to factor many sigma(p^e). We talked about extending the result back then so we both had deep input into the new theory. Recently, after an engineering career in the auto industry in Detroit, I extended Proposition 11 to apply to many more cases in several different ways. I think, Cam, that this is the road you are suggesting. Steve Elmore stevelmore@gmail.com |
||||
