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Nice nt with remainder set

Source: Turkey JBMO TST 2024 P4

May 13, 2024
number theory

Problem Statement

Let nn be a positive integer and d(n)d(n) is the number of positive integer divisors of nn. For every two positive integer divisor x,yx,y of nn, the remainders when x,yx,y divided by d(n)+1d(n)+1 are pairwise distinct. Show that either d(n)+1d(n)+1 is equal to prime or 44.
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