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gcd and positive divisors

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August 9, 2010
number theorygreatest common divisornumber theory unsolved

Problem Statement

Let a a and b b be natural numbers with property gcd(a,b)=1 gcd(a,b)=1 . Find the least natural number k k such that for every natural number r≥k r \ge k , there exist natural numbers m,n>1 m,n >1 in such a way that the number manb m^a n^b has exactly r+1 r+1 positive divisors.
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