Consider the integer 100. It can be completely factored like so:
2^2 x 5^2
Next, consider 3663. It can be completely factored like so:
3^2 x 11 x 37
Finally, consider the integer 31. It is prime, but it can be "completely factored" as just itself, namely 31.
As far as I can tell all these factorizations are unique. Except for the order of the factors, they can be done in one and only one way.
So, prove that the complete factorization of *any* integer into primes is unique.
Charles
2007-01-12
07:54:02
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4 answers
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asked by
Charles
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Mathematics