Example on Linear Diophantine Equation|| Modular Arithmetic||22MATS101-module4||Dr. Sujata T

@mathforall-st1rk
In this video one more important type of example to find solution of linear Diophantine equation is solved.
#drsujatat#engineeringmathematics #modulararithmetic #cryptography #22mats11#module4#

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[samueldeandrade]

Yet another example of some math youtuber overcomplicating a simple problem:

Particular solution: we have to multiply 172 by something with 5 as unit digit. Let's try 5:

172×5 = 860

To get to 1000, we multiply 20 by 7. Done. A particular solution is

(5, 7)

The gcd of 172 and 20 can be easily identified by

172 = 2×86 = 2²×43
20 = 2²×5

So,

gcd(172, 20) = 4.

With that we know the general solution

x = 5-5k
y = 7+43k