AMC 12A Fall 2021 (Problem 12)
What is the number of terms with rational coefficients among the 1001 terms in the expansion of ?
Use 20. Binomial Theorem.
Each term has the form , where .
For to be rational, must be a multiple of 3.
For to be rational, must be even, so must be even.
So must be a multiple of 6.
. There are 167 possible values of .
(C) 167