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n^2 = d_1 + d_2^2+d_3^3 +d_4^4

Source: 2011 Cuba MO 2.3

September 17, 2024
number theoryDivisors

Problem Statement

Let nn be a positive integer and let 1=d1<d2<d3<d41 = d_1 < d_2 < d_3 < d_4 the four smallest divisors of nn. Find alln n such that n2=d1+d22+d33+d44.n^2 = d_1 + d_2^2+d_3^3 +d_4^4.
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