Explanation
Let n = 1, then option (a) , (b) and (d) eliminated. Only option (c) satisfied.
The product of two consecutive number is always even.
nP – n is divisible by p for any natural number greater than 1. It is Fermet’s theorem.
Trick : Let n = 4 and p = 2
Then (4)2 – 4 = 16 – 4 = 12, it is divisible by 2.So, it is true for any natural number greater than 1.
Check through options, the condition is satisfied for all n ∈ N.
Put n = 0, n = 1 and divided by 9.
We get remainder 7.
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