# integers modulo a prime

Create the ring of integers modulo a prime number p as follows.
 i1 : R = ZZ/101 o1 = R o1 : QuotientRing
We can create elements of the ring as follows.
 i2 : 9_R o2 = 9 o2 : R i3 : 103_R o3 = 2 o3 : R
The usual arithmetic operations are available.
 i4 : 9_R * 11_R o4 = -2 o4 : R i5 : 9_R ^ 11 o5 = 49 o5 : R i6 : 9_R * 11_R == -2_R o6 = true
Find the inverse of an integer modulo a prime as follows.
 i7 : 17_R^-1 o7 = 6 o7 : R
To view this element as an element of ZZ use the lift command.
 i8 : lift (17_R^-1, ZZ) o8 = 6