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thereddevils
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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 said: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:
[itex]2^0= 1[/itex]. Remainder on division by 7: 1
[itex]2^1= 2[/itex]. Remainder on division by 7: 2
[itex]2^2= 4[/itex]. Remainder on division by 7: 4
[itex]2^3= 8[/itex]. Remainder on division by 7: 1
[itex]2^4= 16[/itex]. Remainder on division by 7: 2
[itex]2^5= 32[/itex]. Remainder on division by 7: 4
[itex]2^6= 64[/itex]. Remainder on division by 7: 1
[itex]2^7= 128[/itex]. Remainder on division by 7: 2
[itex]2^8= 256[/itex]. Remainder on division by 7: 4
Get the idea?
The purpose of this homework is to practice solving for the remainder when dividing a large integer (2^1000 in this case) by a smaller integer (7 in this case). This type of problem is commonly encountered in mathematics and computer science, and it helps to develop problem-solving skills and understanding of number operations.
In this problem, "remainder" refers to the number left over after dividing (2^1000) by 7. This number can also be described as the part of the original number that does not fit evenly into the divisor.
One way to solve for the remainder is to use the long division method. This involves dividing the number by the divisor, and then multiplying the quotient by the divisor and subtracting it from the original number. The result is the remainder. However, for very large numbers like (2^1000), it may be more efficient to use a calculator or computer program to solve for the remainder.
Yes, there are other methods that can be used to solve for the remainder of (2^1000) / 7. These include modular arithmetic, which involves finding the remainder when dividing by a certain number, and the power rule, which states that the remainder of a number raised to a power can be found by taking the remainder of the number and raising it to the same power.
Solving for the remainder in this problem is important because it allows us to better understand the concept of division and how it applies to large integers. It also has practical applications in fields like computer science, where finding the remainder is necessary for tasks such as hashing and error detection.