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On divisors of n

Source:

September 8, 2010
number theoryDivisorsequationIMO Shortlist

Problem Statement

Find all positive integers nn such that n=d62+d721,n=d_6^2+d_7^2-1, where 1=d1<d2<<dk=n1 = d_1 < d_2 < \cdots < d_k = n are all positive divisors of the number n.n.