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Digits, prime factors, and exponents [Macedonia JBMO TST 2017, P5]

Source: Macedonia JBMO TST 2017, Problem 5

June 26, 2018

number theoryDigitsprime factorsExponents

Problem Statement

Find all the positive integers

n

so that

n

has the same number of digits as its number of different prime factors and the sum of these different prime factors is equal to the sum of exponents of all these primes in factorization of

n

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