Modulo in solving numbers raised to high exponents

  • Context: Undergrad 
  • Thread starter Thread starter yik-boh
  • Start date Start date
  • Tags Tags
    Exponents Numbers
Click For Summary
SUMMARY

The discussion focuses on using modular arithmetic to compare the magnitudes of the numbers 2110, 375, and 549. Participants emphasize the importance of modular reduction techniques for determining which of these exponential expressions is the greatest without the use of logarithms. The consensus is that applying modular methods can simplify the comparison process and yield accurate results.

PREREQUISITES
  • Understanding of modular arithmetic
  • Familiarity with exponentiation
  • Basic knowledge of number theory
  • Ability to perform calculations with large numbers
NEXT STEPS
  • Research "Modular exponentiation techniques"
  • Learn "Chinese Remainder Theorem" for modular comparisons
  • Explore "Fermat's Little Theorem" for simplifying calculations
  • Study "Exponentiation by squaring" for efficient computation
USEFUL FOR

Mathematicians, students studying number theory, and anyone interested in computational methods for comparing large exponential numbers.

yik-boh
Messages
57
Reaction score
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:
Physics news on Phys.org


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:
No. We're not allowed. My teacher told me to use a modular reduction and comparison. Can you teach me how?
 

Similar threads

Undergrad Modulo and Modulus in math and computer programming
  • · Replies 5 ·
Replies
5
Views
3K
How to find the value of a complex number with high exponent
  • · Replies 10 ·
Replies
10
Views
2K
Python Re: Python’s Sympy Module and the Cayley-Hamilton Theorem
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Could Different Attractors Explain Variations in Lyapunov Exponents?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is There a Predictable Pattern in Prime Exponent Series Gaps?
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad Constant raised to complex numbers
  • · Replies 14 ·
Replies
14
Views
2K
High School Fractional/decimal powers
  • · Replies 10 ·
Replies
10
Views
3K
High School Two interesting number theory tricks
  • · Replies 3 ·
Replies
3
Views
2K
Prove ##|\{ q\in\mathbb{Q}: q>0 \} |=|\mathbb{N}|##.
  • · Replies 3 ·
Replies
3
Views
2K
Powers with fractional exponents that have an even denominator
  • · Replies 13 ·
Replies
13
Views
3K