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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

I have hard understanding what we doing when we solve

\(\displaystyle 35y \equiv 13(mod\ 97)\)

I understand we can rewrite that as

\(\displaystyle 35y = 13+97m\)

if we replace \(\displaystyle m=-x\) we got

\(\displaystyle 97x+35y=13\)

I get \(\displaystyle gcd(97,35)=1 \) that means we will have one soloution.

and the diophantine equation got soloution for \(\displaystyle y=-468+97k

\) and what shall I do next?

Regards,