So is 6=-1*-6=-2*-3...
This can get muddy pretty fast.
It depends on what definition you are using.
Most definitions explicitly require p>1 for a prime, but it depends on how you want the Unique Factorization Decomposition theorem to hold.
You can either say that only positive numbers can be prime in which case every integer is up to a unit (1 or -1)uniquely factorizable as a product of primes.
Or you can accept negative primes as primes and say that every integer is uniquely factorizable as a product of primes up to associates (p vs -p).
The point is I've seen many references and sources, even in advanced abstract algebra whose definition of primes would include negative ones.
This can get muddy pretty fast.
It depends on what definition you are using.
Most definitions explicitly require p>1 for a prime, but it depends on how you want the Unique Factorization Decomposition theorem to hold.
You can either say that only positive numbers can be prime in which case every integer is up to a unit (1 or -1)uniquely factorizable as a product of primes.
Or you can accept negative primes as primes and say that every integer is uniquely factorizable as a product of primes up to associates (p vs -p).
The point is I've seen many references and sources, even in advanced abstract algebra whose definition of primes would include negative ones.
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