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h(n) is the greatest prime divisor of n

Source: ILL 1979 - Problem 77.

June 5, 2011
number theory unsolvednumber theory

Problem Statement

By h(n)h(n), where nn is an integer greater than 11, let us denote the greatest prime divisor of the number nn. Are there infinitely many numbers nn for which h(n)<h(n+1)<h(n+2)h(n) < h(n+1)< h(n+2) holds?
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