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.

If negative numbers were allowed -40 on both scales 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.

Posted by Charlie on 2022-01-07 19:11:36