1. The problem is to find the sequence using Euler's theorem. 2. Euler's theorem states that if $a$ and $n$ are coprime (i.e., $\gcd(a,n)=1$), then: $$a^{\phi(n)} \equiv 1 \pmod{n}$$ where $\phi(n)$ is Euler's totient function, which counts the positive integers up to $n$ that are relatively prime to $n$. 3. To use Euler's theorem to find a sequence, we need to know the modulus $n$ and the base $a$. 4. Once $a$ and $n$ are known, compute $\phi(n)$. 5. Then, the sequence of powers of $a$ modulo $n$ will repeat every $\phi(n)$ terms, i.e., $$a^k \equiv a^{k \bmod \phi(n)} \pmod{n}$$ 6. This allows us to find terms in the sequence efficiently by reducing exponents modulo $\phi(n)$. 7. Without specific values for $a$ and $n$, the general approach is: - Compute $\phi(n)$ - For each term $k$, compute $a^{k \bmod \phi(n)} \bmod n$ 8. If you provide specific values for $a$ and $n$, I can compute the sequence explicitly.