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Euclid: Elementa
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PROPOSITION 25. 
 
 
If two numbers be prime to one another, the product of one of them into itself will be prime to the remaining one. 
 
 
Let A, B be two numbers prime to one another, and let A by multiplying itself make C:  I say that B, C are prime to one another. 
   
   
For let D be made equal to A.  Since A, B are prime to one another, and A is equal to D, therefore D, B are also prime to one another.  Therefore each of the two numbers D, A is prime to B; therefore the product of D, A will also be prime to B. [VII. 24]  But the number which is the product of D, A is C.  Therefore C, B are prime to one another.  Q. E. D. 
           
           
 
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