Try this beautiful problem Based on Integer, useful for ISI B.Stat Entrance.
Let n be any integer. Then \(n(n + 1)(2n + 1)\)
Integer
Perfect square numbers
Odd number
Answer: (c) is an integral multiple of 6
TOMATO, Problem 156
Challenges and Thrills in Pre College Mathematics
\(n(n + 1)\) is divisible by \(2\) as they are consecutive integers.
If \(n\not\equiv 0\) (mod 3) then there arise two casess........
Case 1,,
Let \(n \equiv 1\) (mod 3)
Then \(2n + 1\) is divisible by 3.
Let \(n \equiv2\) (mod 3)
Then\( n + 1\) is divisible by \(3\)
Can you now finish the problem ..........
Now, if \(n\) is divisible by \(3\), then we can say that \(n(n + 1)(2n + 1)\) is always
divisible by \(2*3 = 6\)
Therefore option (c) is the correct
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