Find all possible pair(s) (A, B) of positive base 10 digits satisfying this relationship:

(B/A)^o Celsius = (AB)^o Fahrenheit, where AB denotes the concatenation of digits.

Provide valid reasoning for your answer.

*** It may be noted that F = (9/5)*C+32, wher C denotes degree(s) Celsius and F denotes degree(s) Fahrenheit.