Question

P is a prime number greater than 5.what is the remainder when p isdivided by 6.? select one: a. 5 b. 1 c. 1 or 5 d. 4

Answer 1

Answer:

Every integer greater than 3 which is not divisible by 3 is

of the form 3n+1 or 3n+2.

If n is even, say n = 2k then 3n+1 = 3(2k)+1 = 6k+1, which leaves

a remainder of 1 when divided by 6

If n is even, say n = 2k then 3n+2 = 3(2k)+2 = 6k+2, which is even,

so we don't need to consider this case.

If n is odd, say n = 2k+1, then 3n+1 = 3(2k+1)+1 = 6k+3+1 = 6k+4,

which is even, so we don't need to consider this case either.

If n is odd, say n = 2k+1, then 3n+2 = 3(2k+1)+2 = 6k+3+2 = 6k+5,

which leaves a remainder of 5.

So the theorem is proved.