If a and b are integers and 12a = 25b, does 12 | b? does 25 | a? Explain.?

2015-12-17 11:23 am

回答 (2)

2015-12-17 11:26 am
Yes. The prime factorization of the integer "12*a" must equal the prime factorization of the integer "25*b". When both have been fully factored, there will be two 2's and a 3 on the left, which must be duplicated on the right; and there will be two 5's on the right, which must be duplicated on the left.
2015-12-17 11:32 am
You don't have to keep asking this same question with different numbers. The concept and method of proof are exactly the same.


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