Differences of residues (mod p)
نویسندگان
چکیده
منابع مشابه
DECIMATIONS OF -SEQUENCES AND PERMUTATIONS OF EVEN RESIDUES mod p∗
Goresky and Klapper conjectured that for any prime p > 13 and any -sequence a based on p, every pair of allowable decimations of a is cyclically distinct. The conjecture is essentially equivalent to the statement that the mapping x → Axd, with (d, p− 1) = 1, p A, is a permutation of the even residues (mod p) if and only if d = 1 and A ≡ 1 (mod p) for p > 13. We prove the conjecture for p > 2.26...
متن کاملDecimations of l-Sequences and Permutations of Even Residues mod p
Goresky and Klapper conjectured that for any prime p > 13 and any `-sequence a based on p, every pair of allowable decimations of a is cyclically distinct. The conjecture is essentially equivalent to the statement that the mapping x→ Axd, with (d, p− 1) = 1, p A, is a permutation of the even residues (mod p) if and only if d = 1 and A ≡ 1 (mod p), for p > 13. We prove the conjecture for p > 2.2...
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Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite p-local H-spaces of rank l < p−1. The first construction goes through when l = p− 1 and we show the second does as well. However, the space produced need not be an H-space. We give a criterion for when an H-space is obtained. In the special case of rank 2 mod-3 H-spaces, we also give...
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Modular gates are known to be immune for the random restriction techniques of Ajtai Ajt83], Furst, Saxe, Sipser FSS84], Yao Yao85] and H astad H as86]. We demonstrate here a random clustering technique which overcomes this diiculty and is capable to prove generalizations of several known modular circuit lower bounds of Barrington, Straubing, Th erien BST90], Krause and Pudll ak KP94], and other...
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Consider a (MODq;MODp) circuit, where the inputs of the bottom MODp gates are degree-d polynomials with integer coefficients of the input variables (p, q are different primes). Using our main tool — the Degree Decreasing Lemma — we show that this circuit can be converted to a (MODq;MODp) circuit with linear polynomials on the input-level with the price of increasing the size of the circuit. Thi...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1976
ISSN: 0022-314X
DOI: 10.1016/0022-314x(76)90019-6