+1833 Find the smallest positive integer that is greater than $1$ and relatively prime to the product of the first 20 positive integers. Reminder: two numbers are relatively prime if their greatest common divisor is 1.
+33615 Let's call the product of the first 20 positive integers, p.
21 and 22 clearly have common divisors with p (3 and 7 in the case of 21; 2 and 11 in the case of 22).
However, 23 is prime and does not divide p exactly (in fact p/23 has remainder 11), so their greatest common divisor is 1. So 23 is the smallest positive integer that is greater than 1 and relatively prime to p.
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+33615 Let's call the product of the first 20 positive integers, p.
21 and 22 clearly have common divisors with p (3 and 7 in the case of 21; 2 and 11 in the case of 22).
However, 23 is prime and does not divide p exactly (in fact p/23 has remainder 11), so their greatest common divisor is 1. So 23 is the smallest positive integer that is greater than 1 and relatively prime to p.
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