perplexus.info :: Just Math : Celsius- A Fahrenheit Multiple?

Celsius- A Fahrenheit Multiple? (Posted on 2016-06-21)

Find all pairs (N, X) of integers such that:

X^o Celsius = N*X^o Fahrenheit

*** C = 5(F-32)/9, where C and F respectively denotes Celsius and Fahrenheit scales of temperature.

No Solution Yet Submitted by K Sengupta

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Two solutions

| Comment 2 of 7 |

C=5*(F-32)/9

For F congruent 5 (mod 9) C will be an integer (congruent to mod 5).

C/F will be integer when |C| higher or equal than |F|and F also mod 5

F=5 C=-15 N=-3

F =-40 C=-40 N=1

So N,X = (-3,-15) (1,-40)

Edited on June 21, 2016, 5:01 pm

Posted by armando on 2016-06-21 16:51:02

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