**Theorem NT 5.1:** Every natural number $n>1$ is either prime or divisible by a prime.

**Theorem NT 5.2:** Suppose $p$ is prime and $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ are $n$ integers, where $n \geq 2$. If $p \mid a_{1} \cdot a_{2} \cdot a_{3} \cdot \ldots \cdot a_{n},$ then $p \mid a_{i}$ for at least one of the $a_{i}(1 \leq i \leq n)$.

**Theorem NT 5.3:** If $n$ is an integer greater than 1 then $n$ can be written as a product of primes. *(HINT: Prove using strong induction. Consider two cases, when $k+1$ is prime, and when it is composite)*

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