Numbers have different representations depending on the bases on which they are expressed. For example in base 3, the number 12 is written as 110 (1x32 + 1x31 + 0x30), but in base 8 it is written as 14 (1x81 + 4x80). Consider, for example, the integers 12 and 5.
Certainly these are not equal if base 10 is used for each. But suppose 12 was a base 3 number and 5 was a base 6 number then what happens, 12 base 3=1x31 + 2x30, or 5 base 6 or 5 base 10(5 in any base is equal to 5 base 10). So 12 and 5 can be equal if you select the right bases for each of them.
Write a program to input two integers, X and Y, and calculate the smallest base for X and smallest base for Y (likely different from X) so that X and Y represent the same value. The base associated with X and Y will be between 1 and 20 (both inclusive). In representing these numbers the digits 0 to 9 have their usual decimal interpretations. The upper case alphabetic characters A through J represent digits 10 through 19 respectively.
Test your program for the following data and some random data:
INPUT: X=12, Y=5 OUTPUT: 12(base 3) = 5(base 6) INPUT: X=10, Y=A OUTPUT: 10(base 10) = A(base 11) INPUT: X=12, Y=34 OUTPUT: 12(base 17) = 34(base 5)
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