E794  Theorema arithmeticum eiusque demonstratio
(A theorem of arithmetic and its proof)
Summary:
(from the English transltion by Jordan Bell)
In this paper, Euler proves that for m unequal positive integers a,b,c,d,..., the
sum of the fractions: a^n/{(ab)(ac)(ad)...} + b^n/{(ba)(bc)(bd)...} + c^n/{(ca)(cb)(cd)...} + d^n/{(da)(db)(dc)...} + ...
is equal to 0 for n less than or equal to m2, and he gives a general formula for
the sum of these fractions for n equal m1, m and greater than m. He shows a direct
relationship between the values of the sum of these fractions for higher n and the
coefficients of the polynomial (za)(zb)(zc)...
Publication:

Originally published in Commentationes arithmeticae 2, 1849, pp. 588592

Opera Omnia: Series 1, Volume 6, pp. 486  493
 Reprinted in Opera postuma 1, 1862, pp. 152156 [E794a]
Documents Available:
 Original publication: E794
 English translation (Jordan Bell): E794
 Other works that cite this paper include:
 Manuel Ojanguren's and Ivan Panin's paper "Rationally trivial hermitian spaces are locally trivial" in .pdf format.
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