Question

Help solve for x
33x = 60 (mod 97)

Answer 1

x = 90

Answer 2

I know that's the answer, but how did you get that?

Answer 3

I found thatt 33 inverse of mod 97 is 50. What do I do from there?

Answer 4

33x-60=97k
k is an integer
33x-97k=60

97=33(2)+31
33=31(1)+2

so


33-31(1)=2 (rewrote last equation above)
33-[97-33(2)]=2 (rewrote next to last above)
Combining like terms:
3(33)-97=2
60 is a multiply of 2
2 times 30 is 60
multiply both sides by 30
90(33)-30(97)=60

Does that help?
I used euclidean algorithm.
Can you see what x is?

Answer 5

Ohh yes, I get it now. Thanks for the help @myininaya