A ug 2 00 2 ON NON - INTERSECTING ARITHMETIC PROGRESSIONS
نویسنده
چکیده
Let L(c, x) = e c √ log x log log x. We prove that if a 1 (mod q 1), ..., a k (mod q k) are a maximal collection of non-intersecting arithmetic progressions, with 2 ≤ q 1 < q 2 < · · · < q k ≤ x, then x L(√ 2 + o(1), x) < k < x L(1/6 − o(1), x). In the case for when the q i 's are square-free, we obtain the improved upper bound k < x L(1/2 − o(1), x) .
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