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Root Difference and Seventeen Puzzle (Posted on 2015-08-29) Difficulty: 3 of 5
Each of X and Y is a positive integer which is not a perfect square that satisfy:
√X - √Y = √17
Is each of X and Y always divisible by 17?
Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Generalization Comment 3 of 3 |
If x, y and z are integers, and sqrt(x) - sqrt(y) = sqrt(z), 
then x and y are divisible by z whenever z is not divisible by a perfect square.  So, for instance, z = 10 works but z = 12 does not.  This is a simple generalization of the proof I already posted.

Also, if x, y and z are integers, and sqrt(x) + sqrt(y) = sqrt(z),
then x and y are divisible by z whenever z is not divisible by a perfect square. 

  Posted by Steve Herman on 2015-08-30 18:56:06
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