Needs["NumberTheory`NumberTheoryFunctions`"]

ChineseRemainder[{17, 4}, {101, 97}]

ChineseRemainder[{0, 0, 0, 1}, {2, 3, 5, 7}]

CR[{a_, b_}, {p_, q_}] := 
      Module[{g, s, t}, 
{g, {s, t}} = 
          ExtendedGCD[p, q]; 
Mod[b*s*p + a*t*q, 
          p*q]
]

CR[{17, 4}, {101, 97}]

CR[{0, 0}, {2, 3}]

CR[{0, 0}, {2*3, 5}]

CR[{0, 1}, {2*3*5, 7}]

a = Random[Integer, {(10^99), (10^100)}];
b = Random[Integer, {(10^99), (10^100)}];
p = NextPrime[a];
q = NextPrime[b];

CR[{a, b}, {p, q}] // Timing