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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer solution

| Comment 2 of 3 |

for fahr=32:9000000/5+32

celsius=(fahr-32)*5/9;

if celsius==floor(celsius)

prod=fahr*celsius;

sr=round(sqrt(prod));

if sr*sr==prod

disp([celsius fahr]);

end

Celsius   Fahrenheit  Product   Square Root
      0        32             0       0
    200       392         78400     280
   9800     17672     173185600   13160
 460800    829472  382220697600  618240

Posted by Charlie on 2022-01-07 09:55:28

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