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Divisibility question

Source: Balkan MO 1992, Problem 1

April 25, 2006
number theory proposednumber theory

Problem Statement

For all positive integers m,nm,n define f(m,n)=m34n+6−m34n+4−m5+m3f(m,n) = m^{3^{4n}+6} - m^{3^{4n}+4} - m^5 + m^3. Find all numbers nn with the property that f(m,n)f(m, n) is divisible by 1992 for every mm. Bulgaria
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