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Q.

The statement, “Every positive integer can be represented in exactly one way apart from rearrangement as a product of one or more primes” is called ____.


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Detailed Solution

Let us state the fundamental theorem of arithmetic. It states that any integer greater than one is a prime number or is a unique product of prime numbers. We now know that integers include the sets of negative, positive, and zero integers. However, only positive integers are considered in the fundamental theorem of arithmetic, and only after integer 1. That includes 2, 3, 4, 5, and so on indefinitely. Following that, it is stated that integers greater than one, (i.e.) 2, 3, 4, 5, ..., can be expressed as prime numbers or as a product of prime numbers. So, first, let us define a prime number. A prime number has only two factors, which are 1 and itself. It is not divisible by any other number exactly. So, there are examples like 2, 3, 5, 7, ... In this case, 2 is both the smallest prime number and the only even prime number.
 
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