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Q: Need an Algorithm for this Integer problem. Can you figure it out? ( No Answer,   6 Comments )
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 Subject: Need an Algorithm for this Integer problem. Can you figure it out? Category: Science > Math Asked by: zeusdman-ga List Price: \$50.00 Posted: 19 May 2006 09:06 PDT Expires: 18 Jun 2006 09:06 PDT Question ID: 730401
 ```Need an Algorithm for this Integer problem. Can you figure it out? Looking for an algorithm to perform the following mathematical function: Given an INTEGER up to a maximum of 21 digits, decompose the number into a formula like this: X^y + W^v + S^t = Number (X^Y means X to the power of Y and so forth) where the bases X, W, S are integers between [2-255] and the exponents y,v,t are also integers between [0-255]. Lets see if there is a math genius that can figure this out with an algorithm that will work for all numbers up to 21 digits``` Request for Question Clarification by eiffel-ga on 19 May 2006 09:49 PDT ```Hi zeusdman-ga, Would you accept, as an alternative answer, a straightforward proof that this is impossible? Regards, eiffel-ga```
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 Subject: Re: Need an Algorithm for this Integer problem. Can you figure it out? From: rracecarr-ga on 19 May 2006 11:01 PDT
 `You can't get 1 or 2 for starters...`
 Subject: Re: Need an Algorithm for this Integer problem. Can you figure it out? From: bipolarmoment-ga on 19 May 2006 11:27 PDT
 `Why the constraint of 2-255 on the bases?`
 Subject: Re: Need an Algorithm for this Integer problem. Can you figure it out? From: oblok-ga on 19 May 2006 11:50 PDT
 ```Yup - impossible. You want an algorithm to decompose 10^21 different values, but your formula (with constrants) cannot create 10^21 different values. (It can create values much larger than 10^21, but you need your formula to be able to represent ALL different integers up to 10^21.)```
 Subject: Re: Need an Algorithm for this Integer problem. Can you figure it out? From: rracecarr-ga on 19 May 2006 18:33 PDT
 ```Good point oblok. Total number of ways to choose X,W,S,y,v,t is 254^3*256^3 = 2.75E14, more than a million times too small.```
 Subject: Re: Need an Algorithm for this Integer problem. Can you figure it out? From: brix24-ga on 20 May 2006 04:35 PDT
 ```zeusdman, When you write "formulas _like_ this," do you mean to allow a variable number of terms on the left and do you mean to allow repetitions of an exponent, i.e., 3^0=1 3^0 + 2^0=2 but not 3^0 + 3^0 + .... = 1000? (At the moment, I don't know if this will allow a solution; I'm just asking if this interpretation is a possibility.)```
 Subject: Re: Need an Algorithm for this Integer problem. Can you figure it out? From: frde-ga on 20 May 2006 04:46 PDT
 ```@zeusdman-ga I can see what you are getting at. A 6 byte unsigned integer looks like :- Debug.Print Format(255# ^ 6, "#########################") 274941996890625 eg: 15 digits which is a lot less than 21 digits By making the first two bytes into X^Y you can get some incredibly large numbers, but to get a complete range of numbers you need to be able to fill in the 'holes' With two bytes the maximum range that you can 100% describe is 65025 255^1 255 255^2 65025 255^3 16581375 255^4 4228250625 Notice how the jumps become unfillable My guess is that you have a legacy system with a 6 byte Float field (Pascal) and you want to expand its range. Unfortunately pure binary is the only way of storing a precise number, IEEE or BCD will give you a (wildly inaccurate) approximation.```
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