$P$ is a prime number greater than 5. What is the remainder when $P$ is divided by 6?
A5
B1
C1 or 5
DNone of these
Answer & Solution
Correct answer: C. 1 or 5
Any integer can be written as one of $6k, 6k+1, 6k+2, 6k+3, 6k+4,$ or $6k+5$. A prime greater than 5 cannot be divisible by 2 or 3, so it cannot be of the forms $6k, 6k+2, 6k+3,$ or $6k+4$. Thus it must be of the form $6k+1$ or $6k+5$, giving remainder 1 or 5.
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