What's wrong with the RSA statement?

[wxrebecca]

Homework Statement

Use an encoding method in which letters A-Z are represented by two-digit numbers 01-26. Use the RSA method with n=23*31 and e = 3 to encode the message HELP ME. (Split the four letter word in two) Compute the decoding exponent d.

the teacher said there was an error so the problem cannot be solved as stated. he asked us to find out what's wrong and explain why.

Homework Equations

The Attempt at a Solution

here' what i tried.
First we get p=23 q=31 and k=(p-1)*(q-1)=660. and e is not relatively prime to 660. so 3d is not equivalent to 1 mod 660. which is 3d=660t+1 and d cannot be solved as an integer. so we cannot find a decoding exponent d.

 

[lippyka]

The error in the problem is that e (3) is not relatively prime to k (660). The property of RSA requires that e and k must be relatively prime. Therefore, it is impossible to solve the problem as stated because the decoding exponent d cannot be found.