maconvert

Now, that I've eliminated exponents that are over the maximum, the number of equations is 354,960. The bottom line, and this is not a deal breaker, is that the number I want to encode into a 4 character string, must be the sum of one of these 354,960 equations.

The maximum exponent value would be 35 (36 total values including 0). I basically want to create an algorithm that runs through every combination of A^a + B^b + C^c + D^d (1,679,616 total possible equations) and compares each sum to the number I want to represent. When it finds a match, it generates the 4 character code (numbers and/or letters) and presents that to the user. I know that this is a relatively inefficient brute force method and I'm aware that a huge proportion of the results will fall outside of the range that I specified, but that's OK. The algorithm will quit when (if) it finds a match, but even if it takes 2 hours to arrive at a result, that's fine. Speed is not an issue in this case. BTW, to your point regarding the maximums, I guess if I use A = 2, B = 3, C = 5, and D = 7, then I should limit my exponents to 35, 28, 19, and 16 respectively.

Hello, I'm working on a computer problem, but, before I waste too much time going down this road, I thought I should pick the brains of you math geniuses. Basically, I want to be able to represent any number between 1 billion and 42 trillion using just 4 characters (numbers and/or letters). This is what I've come up with so far... A^a + B^b + C^c + D^d = LARGE NUMBER a, b, c, & d are exponent variables that can range from 0 to 35 (0,1,2,...X,Y,Z) A, B, C, & D are bases that are integer constants that never change. Basically, if someone is given the 4 exponent values and the bases are already known, they can extrapolate the number value from that. For example, if I decided to always use A = 2, B = 3, C = 5, and D = 7, the exponent sequence Z9E2 would correspond to 2^26 + 3^9 + 5^14 + 7^2 = 6,170,644,221. So, what I want to know is this: Are there particular values of A, B, C, and D that, depending on the values of a, b, c, and d, can generate every single number between 1 billion and 42 trillion? Is there NO set of 4 base values that can generate every single number between 1 billion and 42 trillion? Will any values of A, B, C, and D work? I look forward to your replies. Thanks in advance!