MathDB

N5

Part of 2019 Pan-African Shortlist

Problems(1)

Each term in the sequence has a new prime divisor

Source: 2019 Pan-African Shortlist - N5

1/18/2021
Let n>1n > 1 be a positive integer. Prove that every term of the sequence n−1,nn−1,nn2−1,nn3−1,… n - 1, n^n - 1, n^{n^2} - 1, n^{n^3} - 1, \dots has a prime divisor that does not divide any of the previous terms.
number theory