... which are prime each to each, then one of these integers (say z) and the sum of the other two (say x+y) are both divisible by q. We ,shall give one other theorem which may be demonstrated by elementary means; namely, the following: V. // p is an odd... Diophantine Analysis - Page 95by Robert Daniel Carmichael - 1915 - 118 pagesFull view - About this book
| Mathematics - 1913
...BULLETIN I have proved the following theorem: If p is an odd prime and the equation x" + y" + 2" = 0 **has a solution in integers x, y, z each of which is...positive integer s, less than %(p — 1), such that** (1) (»+ l)pl = *p'+ 1 mod?3. Professor Birkhoff has called my attention to the fact that condition... | |
| R. D. Carmichael - Mathematics - 2004 - 118 pages
...be demonstrated by elementary means; namely, the following: V. // p is an odd prime and the equation **has a solution in integers x, y, z, each of which...then there exists a positive integer s, less than** %(p—i), such that (s+i)p=sp+imod#3. (28) From Eq. (7) we have This relation and two similar ones... | |
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