Is the Calculation of the Last Digit of 10^1000 Mod 8 Correct?

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In summary, the last digit of 101000 (mod 8) is 0. This can be determined by dividing 101000 by 8 and finding the remainder, which is 0. The last digit is calculated by finding the remainder when 101000 is divided by 8, and it is important because it can reveal patterns and relationships between numbers. The use of mod 8 in this calculation is significant because it allows us to focus on the remainder and is commonly used in computer science and cryptography. The last digit can only be 0 since 101000 is a multiple of 8 and the remainder can only be 0, 1, 2, 3, 4, 5, 6,
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EV33
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Homework Statement


What is the last digit of 101000 (mod 8)

Homework Equations





The Attempt at a Solution



10^2[tex]\equiv[/tex]4 (mod 8)

(10^2)^500[tex]\equiv[/tex] 4^500 (mod 8)

4^2=0 (mod 8)

(4^2)^250[tex]\equiv[/tex]0^250[tex]\equiv[/tex]0 (mod 8)

Thus, the last digit is 0.

Are these steps mathematically legal?
 
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ya, what you have done is absolutely fine
 

FAQ: Is the Calculation of the Last Digit of 10^1000 Mod 8 Correct?

What is the last digit of 101000 (mod 8)?

The last digit of 101000 (mod 8) is 0. This can be determined by dividing 101000 by 8 and finding the remainder, which is 0.

How is the last digit of 101000 (mod 8) calculated?

The last digit of 101000 (mod 8) is calculated by finding the remainder when 101000 is divided by 8. This can be done using modular arithmetic or a calculator.

Why is the last digit of 101000 (mod 8) important?

The last digit of 101000 (mod 8) is important because it can provide insights into patterns and relationships between numbers. It can also be used in various mathematical calculations and proofs.

What is the significance of using mod 8 in this calculation?

The use of mod 8 in this calculation is significant because it allows us to focus on the remainder when dividing by 8, which can reveal patterns and relationships between numbers. Mod 8 is also commonly used in computer science and cryptography.

Can the last digit of 101000 (mod 8) be any other number besides 0?

No, the last digit of 101000 (mod 8) can only be 0 because when dividing by 8, the remainder can only be 0, 1, 2, 3, 4, 5, 6, or 7. Since 101000 is a multiple of 8, the remainder is always 0.

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