Modulo in solving numbers raised to high exponents

In summary, the conversation is about using a modular method to solve numbers raised to high exponents. The speaker asks for help in arranging 2^{110}, 3^{75}, and 5^{49} from greatest to least using a modular reduction and comparison. They mention that they are not allowed to use a calculator and ask for guidance on how to use a modular method to solve the problem.
  • #1
yik-boh
57
0
Modular method in solving numbers raised to high exponents

Arrange the ff from greatest to least:

[itex]2^{110}, 3^{75}, 5^{49}[/itex]



How could I use a modular method to be able to answer that one?

I really need it. Hope you could help me.
 
Last edited:
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  • #2


yik-boh said:
Arrange the ff from greatest to least:

[itex]2^{110}, 3^{75}, 5^{49}[/itex]



How could I use a modular method to be able to answer that one?

I really need it. Hope you could help me.

Are you able to use the calculator to do the question?

If yes , use logarithm .
 
Last edited:
  • #3
No. We're not allowed. My teacher told me to use a modular reduction and comparison. Can you teach me how?
 

Related to Modulo in solving numbers raised to high exponents

1. What is the purpose of using modulo in solving numbers raised to high exponents?

The purpose of using modulo in this context is to find the remainder when a number is divided by another number. This is helpful in solving problems involving large exponents, as it allows us to manipulate the numbers and simplify the calculations.

2. How does modulo help in solving numbers raised to high exponents?

Modulo helps in solving numbers raised to high exponents by reducing the size of the numbers involved in the calculation. This makes the calculation more manageable and can also help identify patterns or repetitions in the results.

3. Can you give an example of how to use modulo in solving numbers raised to high exponents?

Sure, for example, if we want to find the last digit of 3^100, we can use modulo 10. 3^100 = 515377520732011331036461129765621272702107522001, so the last digit would be the remainder when dividing this number by 10, which is 1.

4. Are there any limitations to using modulo in solving numbers raised to high exponents?

One limitation is that it can only be used with positive integers. Additionally, using modulo may not always yield the exact solution, as it only gives the remainder and not the full result. It is important to keep these limitations in mind when using modulo in calculations.

5. How can modulo be applied in real-life situations?

Modulo can be applied in many real-life situations, such as cryptography, computer programming, and statistics. In cryptography, modulo is used to ensure the security of encrypted data. In computer programming, it is used for tasks such as generating random numbers. In statistics, it is used to analyze patterns and trends in data. Overall, modulo is a useful mathematical concept with many practical applications.

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