perplexus.info :: Just Math : So many pairs...

So many pairs... (Posted on 2023-08-24)

Please find all pairs (x, y) satisfying the equation:
16^(x^2+y)+16^(y^2+x)=1

No Solution Yet Submitted by Ady TZIDON

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Solved | Comment 2 of 3 |

This only works if both exponents are -1/4, making the two terms each equal to 1/2.

Since the exponents are equal,
x^2 + y = y^2 + x
(x - y)(x + y + 1) = 0

Try with x=? y
x^2 + x + 1/4 = 0 giving x = y = -1/2.
That does the trick

Posted by FrankM on 2023-08-24 22:16:53

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