MathDB

4

Part of 2017 Grand Duchy of Lithuania

Problems(1)

no of distinct odd prime factors of n(n + 3) is a multiple of 3

Source: 2017 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

10/3/2020
Show that there are infinitely many positive integers nn such that the number of distinct odd prime factors of n(n+3)n(n + 3) is a multiple of 33.
(For instance, 180=22⋅32⋅5180 = 2^2 \cdot 3^2 \cdot 5 has two distinct odd prime factors and 840=23⋅3⋅5⋅7840 = 2^3 \cdot 3 \cdot 5 \cdot 7 has three.)
number theoryoddfactorsmultiple