inverse of 985 mod(φ60131)
I think you may have calculated φ(60131) incorrectly.

60131 has two prime factors: 157, 383
Therefore: φ(60131) = (157-1) * (383-1) = 59592

GCD(985,59592) = 1
59592 =  60 * 985 + 492
  985 =   2 * 492 + 1
  492 = 492 * 1


So to determine the inverse of 985 mod φ(60131):

1 = 985 - 2 * 492
1 = 985 - 2 * (59592 - 60 * 985)
1 = 985 - 2 * 59592 + 120 * 985
1 = 121 * 985 - 2 * 59592


Therefore 121 is the inverse of 985 mod φ(60131).