E794 -- Theorema arithmeticum eiusque demonstratio

(A theorem of arithmetic and its proof)

(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/{(a-b)(a-c)(a-d)...} + b^n/{(b-a)(b-c)(b-d)...} + c^n/{(c-a)(c-b)(c-d)...} + d^n/{(d-a)(d-b)(d-c)...} + ... is equal to 0 for n less than or equal to m-2, and he gives a general formula for the sum of these fractions for n equal m-1, 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 (z-a)(z-b)(z-c)... Publication: Documents Available:

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