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No integer solutions (Posted on 2012-12-10) Difficulty: 2 of 5
Prove that the equation 15x2-7y2=9 has no integer solutions.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (2 votes)

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A slightly faster not so fast | Comment 3 of 4 |
7y^2 = 9 - 15x^2
The right hand side is divisible by 3, so y must be divisible by 3.

But if y is divisible by three, then 9 - 7y^2 is divisible by 9, so x must be divisible by 3.

But xdog has already proved that x and y cannot both be divisible by 3, so we are done.

  Posted by Steve Herman on 2012-12-10 17:48:58
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