Reply to last tweety post:
22x=1(mod27) if 27 divides 1-22x which it does if x=-11: 1-(-11)22=9*27.
Also if x1 and x2 are sols of ax=b(modm), then ax1=ax2(modm) and if (a,m) =1, then you can cancel a to get all sols are = modm. So that x= -38,-11,16,43, .