Any integer bigger than 1 is the multiple of a prime
Jump to navigation Jump to search
Any integer bigger than 1 is the multiple of a prime is a basic result in number theory, which can be proved by Reductio ad absurdum.
Assume there are integers bigger than 1 that are not the multiple of a prime, and let a be the smallest of them. Therefore every integer between 1 and a is the multiple of a prime. If a was a multiple of any number between 1 and a it would therefore also be a multiple of a prime, contradictory to our assumption. But a can neither be a multiple of an integer bigger than itself. So a is only divisible by itself and 1, making it prime, again in contradiction to the assumption. So the assumption has to be false.
|Statement of the claim||Any integer bigger than 1 is the multiple of a prime|
|Level of certainty||Proven|