perplexus.info :: Just Math : Root Difference and Seventeen Puzzle

Root Difference and Seventeen Puzzle (Posted on 2015-08-29)

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.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (2 votes)

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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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