Finding 8 Numbers with phi(n) = 240

[AH05]

Find eight different numbers n with phi(n) = 240.



phi(n) = the number of positive integers less than or equal to n, that are relatively prime to n.

 

[HallsofIvy]

Surely you are aware that you must show what you have tried yourself before anyone can give suggestions?

 

[AH05]

12^12 = (3^12)(2^24)

phi(12^12) = phi(3^12) * phi(2^24) = 2^(24-1) * (2-1) *3^12 *(3-1)
= 2^23 * 3^12 * 2 = 2^24 * 3^12