The proof reduces it to galois-groups and shows some easy properties, which are intuitive in the galois-group domain (only divisor of S_5 is A_5 which is not of

The proof reduces it to galois-groups and shows some easy properties, which are intuitive in the galois-group domain (only divisor of S_5 is A_5 which is not of prime-order). Maybe studying the relationship / reduction to / from polynomial to galois will help