(a) Let n = 1105, so n − 1 = 24 • 69. Compute the values of 269 (mod 1105), 22•69 (mod 1105), 24•69 (mod 1105), 28•69 (mod 1105), and use the Rabin–Miller test to conclude that n is composite.
(b) Use the Rabin–Miller test with a = 2 to prove that n = 294409 is composite. Then find a factorization of n and show that it is a Carmichael number.
(c) Repeat (b) with n = 118901521.
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