What is the remainder of 10^2017 divided by 1001?

1 answer:

5 0

Note: When I use the double equal sign, I mean the triple bar used with modular arithmetic

10^3 = 1000 == -1 (mod 1001)
10^3 == -1 (mod 1001)
(10^3)^672 == (-1)^672 (mod 1001)
(10^(3*672) == 1 (mod 1001)
10^2016 == 1 (mod 1001)
10*10^2016 == 10*1 (mod 1001)
10^2017 == 10 (mod 1001)

Final Answer: 10

You might be interested in

At a sale this week, a suit is being sold for $217. This is a 38% discount from the original price. What is the original price?

34kurt

Answer:

List price (original price) = $350

Discount amount ($ saved) = $133

Step-by-step explanation:

The list price is the sale price ($217) divided by the difference of 1 minus the result of the discount (38%) divided by 100.

3 0

3 years ago

Determine the sign of the some of negative 8 + 11

AVprozaik [17]

Answer:

positive 3

Step-by-step explanation:

-8 + 11 is 3. the other way you can think of it is by subtracting 8 from 11.

8 0

3 years ago

Read 2 more answers

Which inequality is graphed below

Vaselesa [24]

Answer:

$3x-2y < 6$

Step-by-step explanation:

First of all, we need to identify the equation of the line. x and y intercepts are known, so we can quickly write the line as

$\frac x 2 + \frac y{(-3)} = 1 \rightarrow 3x-2y=6$ That gives us the last two options. To solve it let's plug a convenient point - read: the origin - into the equation and see which one holds true. And since for obvious reason $3\cdot 0 -2 \cdot 0 =0 < 6$ the valid solution is the last one.