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Add To Cube, Get Square? (Posted on 2007-08-03)

Is there any perfect cube that becomes a perfect square if you add 7 to it?

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

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first step

| Comment 3 of 10 |

Say x^3 + 7 = y^2.

Then if x is even, y^2 = 3 mod 4.

But y^2 can only = 0 or 1 mod 4, according as y is even or odd.

So x is odd and y is even.

Posted by xdog on 2007-08-03 10:55:31

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