n = 
      Prime[Random[Integer, {1, 200}]] Prime[Random[Integer, {1, 200}]]

\(For[i = 0, i < 100, \(i++\), a = Random[Integer, {1, n - 1}]; 

      b = Mod[a^2, n]; 
Print[{a, b, FactorInteger[b]}]
]\)

aprod = 81476  42718  74436

bprod = (2^9) (3) (5) (7) (43)

GCD[aprod - bprod, n]

FactorInteger[n]