What Is the Product of Primes for the Integer 23?

PsychonautQQ
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Homework Statement


My textbook says any integer greater than 1 is a product of primes. Wouldn't that mean that there are no prime numbers? What is the product of primes that create the integer 23?


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The Attempt at a Solution

 
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PsychonautQQ said:

Homework Statement


My textbook says any integer greater than 1 is a product of primes. Wouldn't that mean that there are no prime numbers? What is the product of primes that create the integer 23?


Homework Equations





The Attempt at a Solution


No. 23, for example, is prime. But it is true that any number that is not prime is a product of primes.
 
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PsychonautQQ said:
any integer greater than 1 is a product of primes

In this case, the plural of the word "primes" can also be singular.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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