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If the given expression is to be an integer , then (1 + 12n2) should be a perfect square.
let (1 + 12n2) = ( 2k + 1 ) 2 [ Its obvious that the no. should be odd]
12n2 = 4k(k+1)
3n2 = k(k+1)
now , k and k+1 are coprime.
so either k should be a multiple of n2 or k+1 should be a multiple of n2
......
Can someone complete the answer ? I can't.
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Moderation Team
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