[7 points] Dene a relation on N as follows:
a b if and only if a has exactly the same set of prime factors as b.
(For example, 12 18 because 12 = 22 3 and 18 = 2 32, but 12 6 30 because
30 = 235, so 30 has a prime factor which is not a factor of 12.) Show that
is an equivalence relation on N.
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