Your question is a little imprecise. In general, when the integers $x_i$'s are bounded above and below, such problems are very difficult to decide whether there is a solution see the Knapsack Problem, the Subset Sum Problem, and Integer Linear Programming.
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2 | addendum after Pete's answer to the unbounded case | ||
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Your question is a little imprecise. In general, such problems are very difficult to decide whether there is a solution see the Knapsack Problem, the Subset Sum Problem, and Integer Linear Programming. |
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