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MathNet 2016-part-01 — 184 problems (EN–VI) Question 91

Math Olympiad Vault · MathNet 2016-part-01 — 184 problems (EN–VI)

Question 91

Prove or disprove each of the following hypotheses:

1. Each sequence of at least two consecutive integers contains a number that is divisible by no prime number less than the amount of members in the sequence.

2. Each sequence of at least two consecutive integers contains a number that is relatively prime to all other members of the sequence.