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A294187
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Numbers k == 77 (mod 120) such that (2*k-1)*2^((k-1)/2), (2*k-1)*3^((k-1)/2) and (2*k-1)*5^((k-1)/2) are congruent to 1 (mod k).
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0
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197, 317, 557, 677, 797, 1277, 1637, 1877, 1997, 2237, 2357, 2477, 2837, 2957, 3557, 3677, 3797, 3917, 4157, 4397, 4517, 4637, 4877, 5237, 5477, 5717, 6197, 6317, 6917, 7517, 7757, 7877, 8117, 8237, 8597, 8837, 9437, 9677, 10037
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OFFSET
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1,1
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COMMENTS
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There are no composite numbers up to 2*10^17. The first composite term is 229467972529064957.
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LINKS
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MAPLE
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a:=k->`if`(k mod 120 = 77 and (2*k-1)*2^((k-1)/2) mod k = 1 and (2*k-1)*3^((k-1)/2) mod k = 1 and (2*k-1)*5^((k-1)/2) mod k = 1, k, NULL): seq(a(k), k=1..50); # Muniru A Asiru, Mar 11 2018
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MATHEMATICA
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k = 77; lst = {}; While[k < 12000, If[Mod[(2k -1) PowerMod[{2, 3, 5}, (k -1)/2, k], k] == {1, 1, 1}, AppendTo[lst, k]]; k += 120]; lst (* Robert G. Wilson v, Feb 13 2018 *)
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PROG
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(PARI) is(n) = n%120==77 &&(2*n-1)* Mod(2, n)^((n-1)\2)==1 &&(2*n-1)* Mod(3, n)^((n-1)\2)==1 &&(2*n-1)* Mod(5, n)^((n-1)\2)==1 \\
(GAP) Filtered([1..11000], k->k mod 120 = 77 and (2*k-1)*2^((k-1)/2) mod k = 1 and (2*k-1)*3^((k-1)/2) mod k = 1 and (2*k-1)*5^((k-1)/2) mod k = 1); # Muniru A Asiru, Mar 11 2018
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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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