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Every prime number of the form 3k + 1 can be represented in the form 6m + 1 (where k, m are integers), When
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- k is odd
- k is even
- k can be both odd and even
- No such from is possible
Correct Option: B
The only one even prime number is 2 and this is not in the form of 3k + 1.
Thus any prime number of the form 3k + 1 is an odd number.
This means 3k must be even number which implies that k must be even number also.
Let k = 2m.
Then a prime of the form 3k + 1 is of the form 3(2m) + 1 = 6m+1.
Every prime number of form 3k + 1 can be represented in the form 6m + 1 only, when k is even.
