Fermat's little theorem states that
![a^p](https://tex.z-dn.net/?f=a%5Ep)
≡a mod p
If we divide both sides by a, then
![a^{p-1}](https://tex.z-dn.net/?f=a%5E%7Bp-1%7D)
≡1 mod p
=>
![a^{17-1}](https://tex.z-dn.net/?f=a%5E%7B17-1%7D)
≡1 mod 17
![a^{16}](https://tex.z-dn.net/?f=a%5E%7B16%7D)
≡1 mod 17
Rewrite
![a^{1000000}](https://tex.z-dn.net/?f=a%5E%7B1000000%7D)
mod 17 as
![=(a^{16})^{62500}](https://tex.z-dn.net/?f=%3D%28a%5E%7B16%7D%29%5E%7B62500%7D)
mod 17
and apply Fermat's little theorem
![=(1)^{62500}](https://tex.z-dn.net/?f=%3D%281%29%5E%7B62500%7D)
mod 17
=>
![=(1)](https://tex.z-dn.net/?f=%3D%281%29)
mod 17
So we conclude that
![a^{1000000}](https://tex.z-dn.net/?f=a%5E%7B1000000%7D)
≡1 mod 17
Answer:
1. The answer for this question is corresponding angles.
2. The answer for this question is alternate interior
Answer:
<em> Anna's wand can cast 70 spells</em>
<em></em>
Step-by-step explanation:
Elsa's wand can cast 53 spells
her wand casts 17 fewer cells than her sister Anna's
Amount of spells cast by Anna's wand = ?
We write the question down in the form of an equation
![x - 17 = 53](https://tex.z-dn.net/?f=x%20-%2017%20%3D%2053)
where
is the amount of spells Anna's wand can cast.
we then proceed to solve by collecting like terms to different sides of the equation. We'll have
![x = 53 + 17](https://tex.z-dn.net/?f=x%20%3D%2053%20%2B%2017)
which leaves us with
![x = 70](https://tex.z-dn.net/?f=x%20%3D%2070)
This means that<em> Anna's wand can cast 70 spells.</em>
The student will have $135 in her bank account at the end of the ninth week. You can fine this out by finding out the amount she deposits a week and to do this you would take the $30 and divide it by 2 because she had $30 at the end of the second week.
30/2=15
So you see that the student deposits $15 each week, so to find out how much money she will have in 9 weeks you will multiply her $15 by 9.
15x9=135
So the student will have $135 at the end of the ninth week.
Add 11 to both sides:
-4=-2t
divide 2 by both sides
2=t
Hope it helps! Comment if you have any questions!