A quick math logic question, please help!?

Question

What is the remainder when 3^2007 is divided by 13?

When I started writing the remainders out, I got
3^3 = Remainder 1
3^4 = R3
3^5 = R9
3^6 = R1
3^7 = R3
3^8 = R9

and i tested a few more but the 1,3,9 remainder pattern continued

now the only problem I am having is trying to decide if 2007 is a 1,3, or 9 remainder


If anyone has any ideas please post them
i really appreciate any help, thanks!

Answer 1

If what you say is true, then when the power is a multiple of 3, the remainder is 1. 2007 is a multiple of 3, therefore the remainder should be 1.

Answer 2

The even multiples of 3 are remainder of 1. 2007 is a multiple of 3, so its a remainder 1.

Answer 3

2007 is divisible by 3. So I guess the remainder is 1.

Answer 4

hi, 7. If x-y=5 and x^2+y^2=15. what's the fee of xy? x - y = 5 (x - y)² = 5² x² - 2xy + y² = 25 x² . . . . .+ y² = 15 --------------------------- . . .-2xy = 10 xy = -5 A)-25 B)-5 <=answer C)-3 8. If x and y are integers, what proportion different ordered pairs (x,y) fulfill the equation 2x+4y=17? 2x could be an excellent extensive style and 4y could additionally be even. The sum of two even numbers is likewise even, so it is going to under no circumstances equivalent 17. A) none <=answer B) one C)2 10. One extensive style is thrice fairly the fee of yet another extensive style. If the sum of those numbers is 3, which of right here may be the fee of the extra beneficial of the two numbers? x + 3|x| = 3 x + 3x = 3 4x = 3 x = 3/4 and 9/4 x - 3x = 3 -2x = 3 x = -3/2 and 9/2 <=extra beneficial extensive style is 4.5 A) -2.25 B).seventy 5 C)4.5 <=answer