Balance of Integer Value: Solving (2^1000) / 7 for Remainder | Homework

[thereddevils]

Homework Statement

How much is the balance if u want to get integer value of ((2^1000) divided by 7))

Homework Equations

The Attempt at a Solution

I need a little hint to start off with an attempt.

 

[HallsofIvy]

Since that is a rather large power of two, I suggest that you start with simple examples and see if you can find a pattern:

$2^0= 1$. Remainder on division by 7: 1
$2^1= 2$. Remainder on division by 7: 2
$2^2= 4$. Remainder on division by 7: 4
$2^3= 8$. Remainder on division by 7: 1
$2^4= 16$. Remainder on division by 7: 2
$2^5= 32$. Remainder on division by 7: 4
$2^6= 64$. Remainder on division by 7: 1
$2^7= 128$. Remainder on division by 7: 2
$2^8= 256$. Remainder on division by 7: 4

Get the idea?

 

[thereddevils]

Since that is a rather large power of two, I suggest that you start with simple examples and see if you can find a pattern:

$2^0= 1$. Remainder on division by 7: 1
$2^1= 2$. Remainder on division by 7: 2
$2^2= 4$. Remainder on division by 7: 4
$2^3= 8$. Remainder on division by 7: 1
$2^4= 16$. Remainder on division by 7: 2
$2^5= 32$. Remainder on division by 7: 4
$2^6= 64$. Remainder on division by 7: 1
$2^7= 128$. Remainder on division by 7: 2
$2^8= 256$. Remainder on division by 7: 4

Get the idea?

Thanks Hallsofivy!