Let $m \in \mathbb{Z}^+$ and let $m = p_1^{e_1}p_2^{e_2}...p_{k-1}^{e_{k-1}}p_k^{e_k}$ by unique prime factorization, where $p_i$ is distinct. Why is it true that $gcd(p_i^{e_i}, p_j^{e_j}) = 1$ for $i \neq j$?
2026-05-16 01:45:37.1778895937
Greatest common divisor of two multiples of prime numbers
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