There is some unique method for this!
and be positive integers such that in base number system is equal to in base number system. What is the smallest valid value of ?
The answer is 16.
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1 solution
Since the two numbers are equal, we have 4 x + 3 = 3 y + 4 which reduces to 4 x = 3 y + 1 Since the digits 3 and 4 appear in both nunbers, both x and y have to be greater than 4. Staring from y = 6 and checking both sides of the equation, the first number of y that satisfies the equation is y = 9. Solving the equation, x = 7. Therefore, our answer is 7 + 9 = 1 6