perplexus.info :: Just Math : Divisibility with lcm and gcd

Divisibility with lcm and gcd (Posted on 2016-08-15)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

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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