- #1
chwala
Gold Member
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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?