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imc

number theory intermediate

Problem

Suppose that is the product of three consecutive integers and that is divisible by . Which of the following is not necessarily a divisor of ?
(A)
(B)
(C)
(D)
Solution
Whenever is the product of three consecutive integers, is divisible by , meaning it is divisible by . It also mentions that it is divisible by , so the number is definitely divisible by all the factors of . In our answer choices, the one that is not a factor of is .
Final answer
D