Math Problem Statement
The value of 310=1 (mod 112 ) is
Solution
To find the value of modulo 112, we need to calculate .
Here's the step-by-step process:
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Calculate :
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Find : We need to divide 59049 by 112 and find the remainder.
Now, multiply 527 by 112 to get the closest multiple:
Subtract this from 59049 to get the remainder:
So, .
Thus, .
Would you like more details or have any questions?
Here are 5 related questions:
- How do you compute using modular exponentiation?
- What are some properties of modular arithmetic that simplify calculations?
- How would the result change if we used a different base, say 5 instead of 3?
- Can we solve for any integer ?
- How does Euler's theorem relate to modular arithmetic?
Tip: In modular arithmetic, breaking down large powers into smaller steps using properties like the Chinese Remainder Theorem can simplify calculations significantly.
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Math Problem Analysis
Mathematical Concepts
Modular Arithmetic
Exponentiation
Formulas
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Theorems
Euler's Theorem
Chinese Remainder Theorem
Suitable Grade Level
Advanced High School
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