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# If R is a unique factorization domain and if a and b in R are relatively prime (i.e.,(a,b) = 1), whenever a divides bc, then a divides c. That is, if R is a unique factorization domain and if a and b in R are relatively prime (i.e., (a,b) = 1), whenever a divides bc then a divides c.

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If R is a unique factorization domain and if a and b in R are relatively prime
(i.e.,(a,b) = 1), whenever a divides bc, then a divides c.
That is, if R is a unique factorization domain and if a and b in R are relatively prime
(i.e., (a,b) = 1), whenever a divides bc then a divides c.

https://brainmass.com/math/number-theory/132134

#### Solution Summary

This solution is comprised of a detailed explanation of the relation between relatively prime elements.
It contains step-by-step explanation of the problem that if R is a unique factorization domain and if a and b in R are relatively prime (i.e.,(a,b) = 1), whenever a divides bc, then a divides c.
Notes are also given at the end.

Solution contains detailed step-by-step explanation.

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