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A082371
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Indices n such that the congruence prime(n)^x + prime(n+1)^x == prime(n+2) mod prime(n+3) has no solution.
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5
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2, 7, 9, 11, 16, 19, 20, 22, 23, 25, 28, 29, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 45, 46, 49, 52, 54, 56, 62, 64, 66, 68, 69, 70, 79, 80, 81, 82, 83, 85, 88, 91, 96, 98, 102, 103, 108, 110, 114, 116, 117, 118, 119, 122, 123, 126, 131, 136, 143, 144, 148, 150, 154
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OFFSET
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1,1
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COMMENTS
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Is this sequence infinite? Proof?
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LINKS
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EXAMPLE
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For index = 7 prime(7) = 17 and 17^x + 19^x ~= 23 mod 29 has no solutions.
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PROG
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(PARI) \No solutions to prime(i)^x+prime(i+1)^x ~= prime(i+2) mod prime(i+3) noanpbn(m, n) = { for(p=1, m, f=0; for(x=0, n, if((prime(p)^x+prime(p+1)^x-prime(p+2))%prime(p+3)==0, f=1) ); if( f==0, print1(p" ")) ) }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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