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Divisibility with lcm and gcd (Posted on 2016-08-15) Difficulty: 3 of 5
Each of X and Y is a positive integer such that:
lcm(X,Y) + gcd(X,Y) = X+Y

Is one of X and Y always divisible by the other?

Provide adequate reasoning for your answer.

No Solution Yet Submitted by K Sengupta    
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Hints/Tips re: Answer and reasoning | Comment 3 of 4 |
(In reply to Answer and reasoning by Paul)

Although the answer seems obvious,- the elegance of your proof vis amazing. 

Many happy returns!

  Posted by Ady TZIDON on 2016-08-16 00:31:58
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