Decode the following message which was sent using mod $m = 7081$ and exponent $k=1789$ (RSA): $ 5192 2604 4222 $ I solved $\phi(7081)=6912$, and then solved the linear equation $1789u-6912v=1$ where $u=85$ and $v=22$.
But then, when I plugged this into $5192^{85} \pmod{7081}$, successive squaring gave me $0$, which is clearly incorrect.
I got: $ 85=2^0+2^2+2^4+2^6 $ $ 5192^1=5192 \pmod{7081}\\ 5192^2=6578 \pmod{7081}\\ 5192^4=5174 \pmod{7081}\\ 5192^8=0 \pmod{7081} $ I also got the other two numbers $(2604, 4222)$ raised to the $8$th power are congruent to $0$. Where did I go wrong in this problem?