منابع مشابه
A Remark on Zoloterav’s Theorem
Let n ≥ 3 be an odd integer. For any integer a prime to n, define the permutation γ a,n of {1,. .. , (n − 1)/2} by γ a,n (x) = n − {ax} n if {ax} n ≥ (n + 1)/2, {ax} n if {ax} n ≤ (n − 1)/2, where {x} n denotes the least nonnegative residue of x modulo n. In this note, we show that the sign of γ a,n coincides with the Jacobi symbol a n if n ≡ 1 (mod 4), and 1 if n ≡ 3 (mod 4).
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1973
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-22-2-125-128