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MathNet 2019-part-07 — 184 problems (EN–VI) Question 105

Math Olympiad Vault · MathNet 2019-part-07 — 184 problems (EN–VI)

Question 105

Consider the collection of lines of the form $y = (k+n)x + (k-n)$ on a plane, where $k, n$ are any integers. Is there a point with integer coordinates that doesn't belong to any of such lines?