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MIXED SUMS OF PRIMES AND OTHER TERMS
, 2009
"... In this paper we study mixed sums of primes and linear recurrences. We show that if m ≡ 2 (mod 4) and m+1 is a prime then (m 2n −1 −1)/(m−1) ̸ = m ..."
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In this paper we study mixed sums of primes and linear recurrences. We show that if m ≡ 2 (mod 4) and m+1 is a prime then (m 2n −1 −1)/(m−1) ̸ = m
ON mCOVERS AND mSYSTEMS
 BULL. AUSTRAL. MATH. SOC. 81(2010), NO. 2, 223–235
, 2010
"... Let A = {as(mod ns)} k s=0 be a system of residue classes. With the help of cyclotomic fields we obtain a theorem which unifies several previously known results related to the covering multiplicity of A. In particular, we show that if every integer lies in more than m0 = ⌊ ∑k s=1 1/ns⌋ members of ..."
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Let A = {as(mod ns)} k s=0 be a system of residue classes. With the help of cyclotomic fields we obtain a theorem which unifies several previously known results related to the covering multiplicity of A. In particular, we show that if every integer lies in more than m0 = ⌊ ∑k s=1 1/ns⌋ members of A, then for any a = 0, 1, 2,... there are at least () m0 sub⌊a/n0⌋ sets I of {1,..., k} with ∑ s∈I 1/ns = a/n0. We also characterize when any integer lies in at most m members of A, where m is a fixed positive integer.