a = Random[Integer, {(10^19), (10^20)}]
b = Random[Integer, {(10^19), (10^20)}]
p = Random[Integer, {(10^19), (10^20)}]

Mod[a + b, p]

Mod[a, p] + Mod[b, p]

Mod[Mod[a, p] + Mod[b, p], p]

Mod[a*b, p]

Mod[a, p]*Mod[b, p]

Mod[Mod[a, p]*Mod[b, p], p]