"An abstract algebra teacher intended to give a typist a list of nine integers that form a group under multiplication modulo 91. Instead, one of the nine integers was left out, so that the list appeared as 1, 9, 16, 22, 53, 74, 79, 81. Which integer was left out?"
It's easy to list all the cosets of (Z mod 91, *), so that cannot possibly what this question is asking about.
- 1=1*1, 9=3*3, 22=2*11, 53=53*1, 74=2*37, 79=79*1, 81=9*9=3*3*3*3
All but one has only two prime factors. Prime Factorization Table was helpful for this...
The differences between each integer is 8, 13, 31, 21, 5, 2
- Nothing special there...
Either there's a trick, or this is insanely easy... (perhaps I'm slow...)
