1. (MON 1) Given a set of 1985 positive integers, none of which has a prime divisor larger than 26, prove that the set has four distinct elements whose geometric mean is an integer.
Solution
1. Since there are 9 primes ( distinct two-element subsets of each having a square as the product of elements. Reasoning as above, we find at least one (in fact many) pair of such squares whose product is a fourth power.
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