Theorem NT 5.1: Every natural number is either prime or divisible by a prime.
Theorem NT 5.2: Suppose is prime and
are
integers, where
. If
then
for at least one of the
.
Theorem NT 5.3: If is an integer greater than 1 then
can be written as a product of primes.
(HINT: Prove using strong induction. Consider two cases, when is prime, and when it is composite)
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