Let be distinct odd primes positive integer
Show that both of these identities cannot be true simultanously:
I have proved it for k=2 but have no idea how to prove it for higher k
If we apply the euler function to the product of , and combined with the second equality, we have:
(&)
thus is not greater than k.
combined with the first equality, gives p is less than the greatest prime among .
from (&), we see that
that is impossible since are distinct odd prime!
is it correct?