SUMS OF THE FORM 1 / x k 1 + · · · + 1 / x kn MODULO A PRIME

نویسنده

  • Ernie Croot
چکیده

Using a sum-product result due to Bourgain, Katz, and Tao, we show that for every 0 < 2 ≤ 1, and every integer k ≥ 1, there exists an integer N = N(2, k), such that for every prime p and every residue class a (mod p), there exist positive integers x1, ..., xN ≤ p satisfying a ≡ 1 x1 + · · ·+ 1 xN (mod p).

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تاریخ انتشار 2004