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A160495
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Irregular triangle of residue classes (mod pq) of primes r such that the cyclotomic polynomial Phi(pqr,x) is flat.
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4
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1, 14, 1, 2, 10, 11, 19, 20, 1, 7, 8, 25, 26, 32, 1, 34, 1, 2, 8, 17, 19, 20, 22, 31, 37, 38, 1, 13, 20, 22, 23, 28, 29, 31, 38, 50, 1, 2, 53, 54, 1, 2, 7, 13, 16, 23, 28, 29, 34, 41, 44, 50, 55, 56, 1, 64, 1, 7, 8, 10, 17, 19, 28, 41, 50, 52, 59, 61, 62, 68
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OFFSET
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1,2
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COMMENTS
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A polynomial is flat if its coefficients are 1, 0, or -1. The values of pq are in sequence A046388. Each row begins with 1 and ends with pq-1. For each number k in a row, the number pq-k is also in the row. Row n has 2*A160496(n) terms. For the pq in sequence A160497, the row has only two terms. By Kaplan's theorems 2 and 3, only the first prime r in each residue class 1..(p-1)(q-1)/2 needs to be checked to determine whether the residue class produces flat cyclotomic polynomials. Is there a simplier method of finding these residue classes?
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LINKS
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EXAMPLE
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The second row (1,2,10,11,19,20) is for pq=21. If r is a prime with r mod pq equal to one of these 6 values, then Phi(21*r,x) is flat.
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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