If I = a2 + b2 + c2, where a and b are consecutive

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If I = a² + b² + c², where a and b are consecutive integers and c = ab, then I is

[CDS II 2020 Mathematics Past paper]

An even number and it is not a square of an integer

An odd number and it is not a square of an integer

Square of an even integer

Square of an odd integer