A number theory problem by Rocco Dalto

Number Theory Level pending

Using a hill cipher, find the \( 5 \times 5 \) matrix \( A \) modulo 26 that replaces the plaintext word \( immunoelectrophoretically \) with the ciphertext word \( phosphatidylethanolamines \), where \( a \rightarrow 0, b \rightarrow 1, \ldots , z \rightarrow 25 \). \(\)

Express the answer as the \( \det(A) \) modulo 26.

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