Multiplying any integer with any prime

[ull]

PS. I don't speak or write english very well. I´m doing my best. Is it still ok to post questions?

a = any integer
b = any prime number

a * b = c

Is there a proof that "c" isn't made up by any other prime factors than the prime factors that make up "a" (except for "b")?

 

[Mandelbroth]

PS. I don't speak or write english very well. I´m doing my best. Is it still ok to post questions?

a = any integer
b = any prime number

a * b = c

Is there a proof that "c" isn't made up by any other prime factors than the prime factors that make up "a" (except for "b")?

It's a result of the fundamental theorem of arithmetic.

 

[MathJakob]

Sinse a prime number can only be divided by 1 and itself, no two numbers can ever equal a prime number. I don't know what the proof is called though. I think the OP wants to know the name of the actual law/proof.

 

[Number Nine]

Sinse a prime number can only be divided by 1 and itself, no two numbers can ever equal a prime number. I don't know what the proof is called though. I think the OP wants to know the name of the actual law/proof.

As Mandelbroth said, the proof is the fundamental theorem of arithmetic, from which the OP's desired result follows immediately.