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Perfect squares (Posted on 2013-02-21) Difficulty: 3 of 5
Find all positive integers n such that 4n+6n+9n is a perfect square.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (1 votes)

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Some Thoughts There is probably no solution | Comment 1 of 2

If there is such a square, it must be worth 1 mod 2, and 1 mod 3. Solutions to 4n+6n+9n are cyclic mod 5 {4,3} but no square is worth 3 mod 5, and cyclic mod 7 {5,0,1,0,5,3}, but no square is worth 3 or 5 mod 7. The upshot of this is that only values of n that are divisible by 3 could potentially qualify as squares. No doubt this process could be continued...

 

 

Edited on February 22, 2013, 3:25 am
  Posted by broll on 2013-02-22 02:47:36

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