Let $S$ be the set of numbers of the form

n(n + 1)(n + 3)(n + 4)(n + 8)(n + 10)(n + 12)

where $n$ is any positive integer.

What is the GCD of the elements of $S$?

onyuIee Aug 27, 2024

#1**0 **

It could have no multiple of 7: (15, 16, 18, 20, 22, 24, 26)

It must have at least 1 multiple of 5: (8, 9, 11, 13, **15**, 17, 19)

It must have at least 2 multiples of 3: (13, 14, **15**, 17, 19, **21**, 23, 25)

It must have at least 1 multiple of 2: (**2**, 3, 5, 7, 9, 11, 13, 15)

Therefore the GCF is 5 * 3 * 3 * 2 = **90**

Maxematics Aug 27, 2024