My textbook says if $b$ is a non-prime number then it can be expressed as a product of prime numbers. But if $1$ isn't prime how it can be expressed as a product of prime numbers?
Prime numbers and expressing non-prime numbers
elementary-number-theorynumber theoryprime numbers
Best Answer
What is the sum of no numbers at all? Zero, of course, since it is the additive identity: $x + 0 = 0$, where $x \neq 0$, or even if it is.
Now, what is the product of no numbers at all? It can't be zero, since, maintaining the stipulation that $x \neq 0$, we have $x \times 0 = 0$, and we said $x \neq 0$. The multiplicative identity is $1$, since $x \times 1 = 1$.
Hence, the product of no primes at all is $1$. The fundamental theorem of arithmetic is a subtlety that's unnecessary for answering your question.