# math

posted by .

Prove that if p is a prime number and p is not equal to 3, then 3 divides p^2 + 2. (Hint: When p is divided by 3, the remainder is either 0,1, or 2. That is, for some integer k, p = 3k or p = 3k + 1 or p = 3k + 2.)

I thought you might do three cases with the three values of p in the hint, plugging them into p^2+2. In two of the cases you get a p^2+2=3a (a some integer) form but for p=3k you do not. Am I approaching this wrong?

• math -

The third case is the simplest, because
3|3k
so you're done!

• math -

On the other hand, since it is a prime ≠ 3, so in fact, the third case does not even arise.

• math -

NO

## Similar Questions

1. ### math induction

prove the product of 4 consecutive integers is always divisible by 24 using the principles of math induction. Could anyone help me on this one?
2. ### math

What is the lowest numberthat has a remainder of 1 when divided by 2 and a remainder of 2 when devided by 3 and a remainder of 3 when divided by 4 and a remainder of 4 when divided by 5?
3. ### Math - repost for Anonymous

Can someone show me the steps to these questions (I will provide the correct answers)?
4. ### math

what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and …
5. ### math

what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and …
6. ### IB HL Math

I need to that if there is better way to prove the following: I am trying to prove that x r = k and k is a multiple of x only when x is prime. I said that if x is non-prime, then: Let a = 6 Let r = 4 6! (6 – 4)! 4! = 3(2) x 5 x 4! …
7. ### Math

How many integers bewteen 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4?
8. ### math

Julie has a mystery number. When she divides the mystery number by 5, the remainder is 1 When she divides the mystery number by 6 the remainder is 4 When she didvides the mystery number by 7 the remainder is 6 What is the smallest …
9. ### Math

How many integers between 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4?
10. ### Math adv function

An unknown polynomial f(x) of degree 37 yields a remainder of 1 when divided by x – 1, a remainder of 3 when divided by x – 3, a remainder of 21 when divided by x – 5. Find the remainder when f(x) is divided by (x – 1)(x – …

More Similar Questions