Solution (source code)

= Solution

Use the agreed text encoding to split the plaintext into integer blocks $m_j\in\{0,\ldots,1072\}$. <RSA> encrypts each block by <modular exponentiation>:
$$
r_j\equiv m_j^{11}\pmod{1073}.
$$
Because $1073=29\cdot37$ is a product of distinct <primes>, its <Euler totient function> is $\varphi(1073)=28\cdot36=1008$. The inverse exponent follows from
$$
11\cdot275=3025=1+3\cdot1008.
$$
Thus \b[a decryption exponent is 275], and the three recovered blocks are
$$
\boxed{m_j\equiv r_j^{275}\pmod{1073},\quad0\leq m_j<1073,\quad j=1,2,3}.
$$
To check every block, including blocks not <coprime> to the modulus, reduce modulo each prime. If $m_j$ is nonzero modulo 29, <Fermat's little theorem> gives $m_j^{3025}=m_j$ because $28\mid3024$; if it is zero the equality is immediate. The same argument works modulo 37 because $36\mid3024$. The <Chinese remainder theorem> then gives the equality modulo 1073. Finally reverse the agreed text encoding. The symbols $r_1,r_2,r_3$ are unspecified, so there are no numerical message blocks to evaluate further.