Find integer root in a given range of an equation

Question

Khanh 2011-11-21

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https://ww2.mathworks.cn/matlabcentral/answers/21851-find-integer-root-in-a-given-range-of-an-equation

Given an equation $\sum_{i=1}^{n} C_{ij}*(x_i - k_i)^2 = R$ with C is a covariance n*n matrix of vector x; R and vector k is given.
It's obvious that there are infinite number of real roots for this equation.
However, I wonder if I'm only interesting in integer roots which are in the range between some value [a, b], then is there any function in Matlab that can find them? 
I'm looking at fsolve function but I don't see anyway to specify the conditions that I need (i.e. integers in a certain range).
Does any one have any suggestion, please?
Thanks,

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Khanh 2011-11-21

I see the brute force solution would be checking all the possible solutions which is (b-a)^n which is all the possible integer vectors of vector x. However, I wonder if there is any better way to solve it?

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Answer 1

Walter Roberson 2011-11-21

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Remap the search space to be between 1 and (1 + (b-a+)/2^53), and then the adjacent floating point numbers within that space would correspond exactly to integers over a to b.

I make no representation that this would be efficient.