Problem: Let S be the set of all numbers which are the sum of the squares of three consecutive integers. Then we can say that
Answer Choices:
A. No member of S is divisible by 2
B. No member of S is divisible by 3 but some member is divisible by 11
C. No member of S is divisible by 3 or by 5
D. No member of S is divisible by 3 or by 7
E. None of these
Solution:
Let the consecutive integers be . Then the sum of their squares is which is never divisible by but is when and is then divisible by as required in . Choices , and are eliminated by taking the middle integer equal to , and respectively.