Learned a new proof of the infinitude of primes this morning.
"Saidak argues the infinitude of primes as follows. Let (a_0 = 1), and define (a_n = a_{n−1}\left(a_{n−1} + 1\right)) for (n \ge 1). Since (a_n) and (a_n + 1) have no common divisors, it follows that (a_n) has at least one more prime factor than (a_{n-1}), and thus by induction, (a_n) has at least (n) distinct prime factors."
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