You can type out or hand$-$write your solution. In any event, it must be uploaded and attached in a legible format $($e$.$g$.$ a clear photo, scan, or document$).$

Given the following parameters for an RSA encryption algorithm, determine the public key and the private key. Show all calculation steps, including each iteration. Use proper notation and clearly indicate what you are calculating when solving for the private exponent.

Use prime numbers $457$ and $293$; use $137$ as the public exponent.