a.

By Fermat's little theorem, we have


5 and 7 are both prime, so
and
. By Euler's theorem, we get


Now we can use the Chinese remainder theorem to solve for
. Start with

- Taken mod 5, the second term vanishes and
. Multiply by the inverse of 4 mod 5 (4), then by 2.

- Taken mod 7, the first term vanishes and
. Multiply by the inverse of 2 mod 7 (4), then by 6.


b.

We have
, so by Euler's theorem,

Now, raising both sides of the original congruence to the power of 6 gives

Then multiplying both sides by
gives

so that
is the inverse of 25 mod 64. To find this inverse, solve for
in
. Using the Euclidean algorithm, we have
64 = 2*25 + 14
25 = 1*14 + 11
14 = 1*11 + 3
11 = 3*3 + 2
3 = 1*2 + 1
=> 1 = 9*64 - 23*25
so that
.
So we know

Squaring both sides of this gives

and multiplying both sides by
tells us

Use the Euclidean algorithm to solve for
.
64 = 3*17 + 13
17 = 1*13 + 4
13 = 3*4 + 1
=> 1 = 4*64 - 15*17
so that
, and so 
Answer:
= 78
= 3.5
Step-by-step explanation:
First we need to find
.
We can use the equation
to solve for
.
We can then change that equation to
, since the Commutative Property of Addition says that you can have any addition in any order.
Now, we can solve the equation.

Now that we solved
, we can now solve for
.
Since 25 equals
, we can solve the equation
.
Here is how you solve it:

Since
equals 3.5, which is the simplest form, that is the answer.
Hope this helps, and please mark me brainliest! :)
Question A: The per capita debt would be $43,888.75.
Per capita means the amount per person. To find this amount, we need to take the total debt and divide it by the number of people.
13,561,623 divided by 309 = 43,888.75
For Question B, you will need to have the other CPI value from the table.
Answer:
true
Step-by-step explanation: