perplexus.info :: Just Math : Fahrenheit*Celsius equals Perfect Square

Fahrenheit*Celsius equals Perfect Square (Posted on 2022-01-07)

Each of x and y is a nonnegative integer such that:

x^o Celsius = y^o Fahrenheit

Determine all pairs (x,y) such that x*y is a perfect square, where x < 10⁶

**** Celsius to Fahrenheit conversion is given here.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(x y) = (0,32), (200, 392), (9800, 17672), 460800, 829472)
If negative numbers were allowed, -40 on both sides of the scale would result in the perfect square 1600; this is the only negative that would work in actual possible temperatures (above absolute zero), though the arithmetically correct -1440 °C , -2560 °F produce 3686400, the square of 1920 satisfies the formula.
For an explanation, refer to the solution submitted by Charlie here and here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Just a note	Charlie	2022-01-07 19:11:36
computer solution	Charlie	2022-01-07 09:55:28
Solution	Larry	2022-01-07 08:46:39

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