a) Use Exercise 48 to show that every integer of the form (6m + 1)(l2m + 1)(l8m + 1), where m is a positive integer and 6m + 1, 12m + 1, and 18m + 1 arc all primes, is a Carmichael number.

b) Use part (a) to show that 172,947,529 is a Carmichael number.

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