task2 == Select[Range@100, Co9eff[#] == Co9eff[#^2] &]
   True

Select[Range@100, Co9eff[#, 17] == Co9eff[#^2, 17] &]
   {1, 16, 17, 32, 33, 48, 49, 64, 65, 80, 81, 96, 97}