perplexus.info :: Just Math : Simultaneous Surmise

Simultaneous Surmise (Posted on 2014-11-29)

Each of X and Y is a positive integer.

Can X² +Y+2 and Y² + 4X be simultaneously perfect squares?

If so, provide an example.
If not, prove it.

See The Solution Submitted by K Sengupta

Rating: 3.6667 (3 votes)

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re: Finally!

Comment 3 of 3 |

(In reply to Finally! by Math Man)

Y^2+4X=Y^2+2Y+2, which is never a square for positive Y.

Yes, because (2X-1)^2+4X =z^2 is equivalent to (2X)^2+1 = z^2.

Nice solution.

Posted by broll on 2014-11-29 22:28:33

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