- #1

chwala

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- Homework Statement
- how do we find the inverse of 1973 given gcd (132,289,1973)

- Relevant Equations
- modular arithmetic and co prime...

##132,289≡1973* 67 + 98##

##1973≡98*20+13##

##98≡13*7+7##

##13≡7*1+6##

##7≡6*1+1##

now in reverse my attempt is as follows,

##1≡7-6##

## 1≡7-(13-7)##

##1≡2*7-(1973-20*132,289+1340*1973)##

##1≡2*7-(1341*1973-20*132,289##

which is correct but my interest is in finding the inverse of 1973 help?

##1973≡98*20+13##

##98≡13*7+7##

##13≡7*1+6##

##7≡6*1+1##

now in reverse my attempt is as follows,

##1≡7-6##

## 1≡7-(13-7)##

##1≡2*7-(1973-20*132,289+1340*1973)##

##1≡2*7-(1341*1973-20*132,289##

which is correct but my interest is in finding the inverse of 1973 help?