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 A094595 Number of solutions to 1 == nxy (mod z) == nyz (mod x) == nzx (mod y) with 0 < x < y < z. 1
 1, 2, 6, 5, 17, 3, 31, 7, 23, 5, 47, 5, 60, 14, 20, 12, 78, 12, 78, 9, 35, 18, 91, 9, 74, 19, 50, 9, 119, 7, 110, 38, 56, 30, 65, 9, 170, 41, 66, 12, 169, 16, 143, 36, 55, 17, 162, 12, 143, 19, 55, 28, 171, 13, 113, 23, 71, 32, 201, 6, 265, 50, 59, 45 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Prime values of n yield many more solutions than composite values. If (x,y,z) is a solution, then (nx,ny,nz) is a solution of the equations in A094185. All solutions appear to be in the polytope n < x <= 2n+1, x < y <= 2n^2+2n-1, y < z <= n^4+2n^3+2n^2+n-1. LINKS EXAMPLE a(2) = 2 because there are 2 solutions: (x,y,z) = (3, 7, 41) and (3, 11, 13). MATHEMATICA Table[cnt=0; Do[d=Divisors[n*x*y-1]; Do[z=d[[i]]; If[z>y && Mod[n*x*z, y]==1 && Mod[n*y*z, x]==1, cnt++ ], {i, Length[d]}], {x, 2n+1}, {y, x+1, 2n^2+2n-1}]; cnt, {n, 64}] CROSSREFS Cf. A094185 (number of solutions to n = xy (mod z) = yz (mod x) = zx (mod y) with 0

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Last modified January 20 10:33 EST 2022. Contains 350472 sequences. (Running on oeis4.)