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A083955
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Numbers n > 1 such that n^5 - 2 has no prime factor > n.
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6
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3557, 12038, 14810, 15424, 28456, 30742, 31540, 37665, 45602, 46883, 47879, 48152, 52196, 52617, 55265, 57902, 68306, 69032, 74925, 76262, 79562, 79984, 84569, 90442, 104867, 104956, 107213, 112570, 114614, 119477, 127634, 131072, 132466
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OFFSET
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1,1
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COMMENTS
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Also integers n > 1 for which there is no prime p > n such that x = n is a solution mod p of x^5 = 2, since the following equivalences hold for n > 1: There is a prime p > n such that n is a solution mod p of x^5 = 2 iff n^5 - 2 has a prime factor > n; n is a solution mod p of x^5 = 2 iff p is a prime factor of n^5 - 2 and p > n.
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LINKS
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EXAMPLE
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12038 is a term since 12038^5 - 2 = 252796871460867395166 = 2*3*3*3*263*571*641*911*5849*9127 has no prime factor > 12038.
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MATHEMATICA
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t = {}; Do[If[Max[First/@FactorInteger[n^5-2]]<n, AppendTo[t, n]], {n, 2, 5*10^4}]; t (* Jayanta Basu, May 20 2013 *)
Select[Range[2, 133000], Max[FactorInteger[#^5-2][[;; , 1]]]<=#&] (* Harvey P. Dale, Mar 02 2023 *)
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PROG
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(PARI) {for(n=2, 133000, f=factor(n^5-2); if(f[matsize(f)[1], 1]<=n, print1(n, ", ")))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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