# Integer Relation Among Integers (Integer Relation)

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## Description

Given a vector $x \in \mathbb{Z}^n$, find an integer relation, i.e. a non-zero vector $m \in \mathbb{Z}^n$ such that $<x, m> = 0$

## Related Problems

Generalizations: Integer Relation Among Reals

## Parameters

$n$: dimensionality of vectors

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

HJLS algorithm | 1986 | $O(n^{3}(n+k))$ | $O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable | Exact | Deterministic | Time |