Name of a property in number theory

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I want to find the name (or author of the proof) on the following property:
If $ntimes m=prod_i p_i$ where the $p_i$ are prime numbers, then $n=prod_iin Ip_i$ for some subset $I$.



I know it is a classical result and I know how to prove it, I just need its name (or author).




number-theory reference-request prime-numbers terminology




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  • 7




    I don't think this easy consequence of unique factorisation has a name of its own.
    – Rob Arthan
    2 days ago






  • 1




    It's closely related to Euclid's lemma
    – rtybase
    2 days ago










  • Ok. Thanks. I thought it could be the rephrase of another property more than a consequence. But maybe you are right.
    – Alejandro Díaz-Caro
    2 days ago














up vote
0
down vote

favorite












I want to find the name (or author of the proof) on the following property:
If $ntimes m=prod_i p_i$ where the $p_i$ are prime numbers, then $n=prod_iin Ip_i$ for some subset $I$.



I know it is a classical result and I know how to prove it, I just need its name (or author).




number-theory reference-request prime-numbers terminology




share|cite|improve this question

















  • 7




    I don't think this easy consequence of unique factorisation has a name of its own.
    – Rob Arthan
    2 days ago






  • 1




    It's closely related to Euclid's lemma
    – rtybase
    2 days ago










  • Ok. Thanks. I thought it could be the rephrase of another property more than a consequence. But maybe you are right.
    – Alejandro Díaz-Caro
    2 days ago












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I want to find the name (or author of the proof) on the following property:
If $ntimes m=prod_i p_i$ where the $p_i$ are prime numbers, then $n=prod_iin Ip_i$ for some subset $I$.



I know it is a classical result and I know how to prove it, I just need its name (or author).




number-theory reference-request prime-numbers terminology




share|cite|improve this question













I want to find the name (or author of the proof) on the following property:
If $ntimes m=prod_i p_i$ where the $p_i$ are prime numbers, then $n=prod_iin Ip_i$ for some subset $I$.



I know it is a classical result and I know how to prove it, I just need its name (or author).





number-theory reference-request prime-numbers terminology





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 2 days ago









joriki

164k10179328




164k10179328









asked 2 days ago









Alejandro Díaz-Caro

1011




1011







  • 7




    I don't think this easy consequence of unique factorisation has a name of its own.
    – Rob Arthan
    2 days ago






  • 1




    It's closely related to Euclid's lemma
    – rtybase
    2 days ago










  • Ok. Thanks. I thought it could be the rephrase of another property more than a consequence. But maybe you are right.
    – Alejandro Díaz-Caro
    2 days ago












  • 7




    I don't think this easy consequence of unique factorisation has a name of its own.
    – Rob Arthan
    2 days ago






  • 1




    It's closely related to Euclid's lemma
    – rtybase
    2 days ago










  • Ok. Thanks. I thought it could be the rephrase of another property more than a consequence. But maybe you are right.
    – Alejandro Díaz-Caro
    2 days ago







7




7




I don't think this easy consequence of unique factorisation has a name of its own.
– Rob Arthan
2 days ago




I don't think this easy consequence of unique factorisation has a name of its own.
– Rob Arthan
2 days ago




1




1




It's closely related to Euclid's lemma
– rtybase
2 days ago




It's closely related to Euclid's lemma
– rtybase
2 days ago












Ok. Thanks. I thought it could be the rephrase of another property more than a consequence. But maybe you are right.
– Alejandro Díaz-Caro
2 days ago




Ok. Thanks. I thought it could be the rephrase of another property more than a consequence. But maybe you are right.
– Alejandro Díaz-Caro
2 days ago















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