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4 digit no = 2^m3^n(m + n)

Source: 2016 Romanian NMO grade VII P3

September 3, 2024
number theoryprime factorization

Problem Statement

Find all the positive integers pp with the property that the sum of the first pp positive integers is a four-digit positive integer whose decomposition into prime factors is of the form 2m3n(m+n)2^m3^n(m + n), where m,n∈N∗m, n \in N^*.
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