Given a set
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
of
![1985](/media/m/a/e/e/aee988f0416cd45280623323093e7722.png)
positive integers, none of which has a prime divisor larger than
![26](/media/m/e/4/a/e4af7c2c4cb0031294e6db3d752dd03f.png)
, prove that the set has four distinct elements whose geometric mean is an integer.
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Given a set $M$ 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.