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A350916
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Positive integers k such that (k+1)^4 has a divisor congruent to -1 modulo k.
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13
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1, 2, 3, 5, 9, 11, 14, 17, 29, 35, 41, 43, 59, 65, 69, 125, 134, 139, 174, 194, 339, 386, 449, 461, 681, 901, 937, 1169, 1322, 1325, 1715, 1971, 2211, 3054, 6395, 7989, 8857, 9077, 10849, 11483, 12545, 13082, 20909, 21506, 23861, 35233, 54734, 62210, 66923, 89045, 129494, 143289, 172899, 174725, 203321, 332315, 375129, 390051, 426389, 493697, 561513, 982094
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OFFSET
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1,2
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COMMENTS
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For (k+1)^3 similar sequence is finite {1, 2, 3, 5, 9, 11, 14}, while for (k+1)^2 it is just {1, 2, 3, 5}. Starting with power 4 (this sequence), the number of values of k is infinite. One series of values for power 6 is given by A001570.
Only terms 1, 2, 5, 9, 11, 14, 29 are shared between two or more sequences, all others come from exactly one sequence.
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LINKS
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PROG
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(PARI) { for(k=1, 10^6, fordiv((k+1)^4, d, if(Mod(d, k)==-1, print1(k, ", "); break)) ); }
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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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