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Independent Sequence


An infinite sequence {a_i} of positive integers is called weakly independent if any relation sumepsilon_ia_i with epsilon_i=0 or +/-1 and epsilon_i=0, except finitely often, implies epsilon_i=0 for all i.

An infinite sequence {a_i} of positive integers is called strongly independent if any relation sumepsilon_ia_i, with epsilon_i=0, +/-1, or +/-2 and epsilon_i=0 except finitely often, implies epsilon_i=0 for all i.


See also

Strongly Independent, Weakly Independent

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References

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 136, 1994.

Cite this as:

Weisstein, Eric W. "Independent Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IndependentSequence.html

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