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An integer $p\in{\mathbb Z}$ is prime if $p\not=0, 1, -1$ and the only divisors of $p$ are $1, -1, p, -p$.

Which of the following statements is correct?

Every integer is a product of primes.

Every integer except $-1$, $0$, and $1$ is a product of primes.

Every integer $n>1$ can be written in only one way as a product of positive primes.

If $n=p_1p_2p_3=q_1q_2q_3$ where $p_1

then $p_i=q_i$, $i=1,2,3$.

If $n=p^4=q^4$, where $p,q$ are primes, then $p=q$.