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Sum of squares of three consecutive integers

Source: 1970 AHSME Problem 4

March 20, 2014
AMC

Problem Statement

Let SS be the set of all numbers which are the sum of the squares of three consecutive integers. Then we can say that:
<spanclass=′latex−bold′>(A)</span>No member of S is divisible by 2<span class='latex-bold'>(A) </span>\text{No member of }S\text{ is divisible by }2\qquad
<spanclass=′latex−bold′>(B)</span>No member of S is divisible by 3 but some member is divisible by 11<span class='latex-bold'>(B) </span>\text{No member of }S\text{ is divisible by }3\text{ but some member is divisible by }11\qquad
<spanclass=′latex−bold′>(C)</span>No member of S is divisible by 3 or 5<span class='latex-bold'>(C) </span>\text{No member of }S\text{ is divisible by }3\text{ or }5\qquad
<spanclass=′latex−bold′>(D)</span>No member of S is divisible by 3 or 7<span class='latex-bold'>(D) </span>\text{No member of }S\text{ is divisible by }3\text{ or }7\qquad
<spanclass=′latex−bold′>(E)</span>None of these<span class='latex-bold'>(E) </span>\text{None of these}
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