Question

Except for the first two terms,each term of the sequence 1000,x,1000-x,... is obtained by subtracting the...

Except for the first two terms,each term of the sequence 1000,x,1000-x,... is obtained by subtracting the preceding term from the one before that. The last term of the sequence is the first negative term. What positive integer x produces a sequence of maximum length?

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