1. ## Prove not cyclic

Let p and q be odd primes and let m and n be positive integers. Prove that U(p^m) + U(a^n) is not cyclic.
(+ is the external direct product (+ with a circle around it))

2. Originally Posted by mandy123
Let p and q be odd primes and let m and n be positive integers. Prove that U(p^m) + U(a^n) is not cyclic.
(+ is the external direct product (+ with a circle around it))
I think you mean to say $U(p^m) \times U(q^n)$. Since $p,q$ are odd it means $2$ divides both $|U(p^m)|,|U(q^m)|$. And therefore $\gcd( |U(p^m)|,|U(q^m)|) \not = 1$. Thus, their product cannot be cyclic.

### let p and q be odd primes and let m and n be positive integers

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