For the following question please give specific details and steps. Please proof

Question

For the following question please give specific details and steps. Please proof for the fundamental theorem of arithmetic that every single integer that is greater then one can be written as a product of primes and that it is also unique product and also up to arrangement of multiples. For the following question please give specific details and steps. Please proof for the fundamental theorem of arithmetic that every single integer that is greater then one can be written as a product of primes and that it is also unique product and also up to arrangement of multiples.

Explanation / Answer

We will prove it by induction method.

So for n=2 this is true.

Now suppose the statement is true for n= 2,3,...,k

If (k+1) is prime, then we are done.

Uniqueness:

Assume that integer m is the product of prime numbers in two different ways, m = p1. p2...pr= q1.q2...qs

p1 | m = q1.q2...qs and as p1 is prime then p1 divide only one of the primes. Let q1 is the prime such that   p1= q1. By the same method, we get pr= qs  so r=s .

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