fermats last theorem for $p=83$

Question

Prove the first case of fermat's last theorem for the prime $p=83$. If I let $\theta =2p+1$ then $\theta$ is $2\times83+1=167$ where $\theta$ is a prime.
Computing their remainders on division by $83$ we get $1^{83}=1\equiv1(\mod {83})$. Any number greater than $1$ to the power of $83$ gets to large, is there another method to solve it for numbers $\geq$ 2?. Thank you.