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MathNet 2015-part-02 — 191 problems (EN–VI) Question 151

Math Olympiad Vault · MathNet 2015-part-02 — 191 problems (EN–VI)

Question 151

Let $n$ be a natural number such that $n + 1$, $n + 3$, $n + 7$ and $n + 9$ are prime numbers, and $n + 31$, $n + 33$, $n + 37$ and $n + 39$ are also prime numbers. Find the remainder of $n$ divided by 210.