nooby question.
- I heard many times that 0 is a pair number.
- I'm fairly sure that the definition of pair is multiple of 2.
- Yet I heard too that multiples of a prime number p are only 1 and p, therefore excluding 0.
So in the above contradiction, where is/are the false argument/s? I feel like despite what I heard, 0 is not a pair number or maybe only in informatics (that I started studying) which is still weird (the divergence I mean)
Thanks for your time.
$\endgroup$ 32 Answers
$\begingroup$Multiples of a prime number (or of any other number) are $\ldots,-2p,-p,0,p,2p,\ldots$ while the divisors of a prime number are only $\pm1,\pm p$ and the positive divisors are just $1,p$. So there is no contradiction.
$\endgroup$ 1 $\begingroup$There is no contradiction.
We say that $k$ is even if there is some $n$ such that $k=2n$. Zero is even because $0=2\cdot 0$.
We say that $p$ is a prime number if whenever $p=m\cdot n$ and $m\neq p$ then $m=1$. Zero is not a prime number because $0=3\cdot 0$ and $3\neq 0$ but $3\neq 1$.
While zero itself is not a divisor of any number, in fact we have that any number divides zero. Therefore to the question in the title, yes: zero is a multiple of any number.
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