Let n = rs, where r and s are distinct odd primes. Show that there is...

Question

Question

Let n = rs, where r and s are distinct odd primes. Show that there is not a primitive root modulo n.

(Solve through letting L = LCM(r − 1, s − 1). Show that the order of any element of (Z/nZ)∗ is at most L, and that L < φ(n).)

Answer 1

Answer #1

The following way as mentioned above the statement is proved

1) (Z/rsZ) has all elements of order less than (r-1)(s-1)

2) L<phi(n)

Ist of all it can be shown that, 71./87) * ~ /m2)* * ( 7 /»7)* taking the map of (a,b). where e is the element such that a C

But $(n) = 8 (+5) = 25 (1-2) (1-2) (x-1) (8.1). (P-1) is even and lem (8-1, 0-1) - (&-1) is even a (x-1). (8-1). [as eem of o

Note: If you need help to prove of the mapping to be an isomorphism as provided in the answer let me know.

Hope it helps :-)

Answer 2

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