How to Solve a Modular Arithmetic Equation

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SUMMARY

The discussion focuses on solving the modular arithmetic equation 59x + 15 ≡ 6 mod 811. The first step involves simplifying the equation to 59x ≡ -9 mod 811. Participants clarify that two numbers a and b are equivalent in modular arithmetic if a - b = m*n for some integer m. The solution requires finding the multiplicative inverse of 59 modulo 811 to isolate x.

PREREQUISITES
  • Understanding of modular arithmetic principles
  • Familiarity with solving linear congruences
  • Knowledge of multiplicative inverses in modular systems
  • Basic algebraic manipulation skills
NEXT STEPS
  • Research how to find the multiplicative inverse using the Extended Euclidean Algorithm
  • Study examples of solving linear congruences in modular arithmetic
  • Learn about the properties of modular arithmetic and equivalence classes
  • Explore applications of modular arithmetic in cryptography
USEFUL FOR

Students studying number theory, mathematicians interested in modular arithmetic, and anyone solving linear congruences in mathematical or computational contexts.

viviane363
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Homework Statement



compute 59x +15 [tex]\equiv[/tex] 6 mod 811

Homework Equations





The Attempt at a Solution



59x [tex]\equiv[/tex] -9 mod 811
I really don't know hoow to do from here.
 
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so i think 2 numbers a,b are equivalent in modular arthimetic, mod n, if

a-b = m*n for some integer m

in your case this translates to
59x+9 = 811.m
 

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