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Books Books 1 - 2 of 2 on ... which are prime each to each, then one of these integers (say z) and the sum....  
" ... 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 95
by Robert Daniel Carmichael - 1915 - 118 pages
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Bulletin of the American Mathematical Society

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...
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The Theory of Numbers and Diophantine Analysis: Two Volumes Bound As One

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 %(pi), such that (s+i)p=sp+imod#3. (28) From Eq. (7) we have This relation and two similar ones...
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