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d_7^2+d_{10}^2=(n/d_{22})^2

Source: 1998 Belarus TST 5.3

December 25, 2020
number theoryDivisors

Problem Statement

Let 1=d1<d2<d3<...<dk=n1=d_1<d_2<d_3<...<d_k=n be all different divisors of positive integer nn written in ascending order. Determine all nn such that d72+d102=(n/d22)2.d_7^2+d_{10}^2=(n/d_{22})^2.
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