It may appear that RSA decryption does not work if you are unlucky enough to choose a message a that is not relatively prime to m. Of course, if m = pq and p and q are large, this is very unlikely to occur.
(a) Show that in fact RSA decryption does work for all messages a, regardless of whether or not they have a factor in common with m.
(b) More generally, show that RSA decryption works for all messages a as long as m is a product of distinct primes.
(c) Give an example with m = 18 and a = 3 where RSA decryption does not work. [Remember, k must be chosen relatively prime to φ(m) = 6.]
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