Corollary: Prime Dividing Product of Primes Implies Prime Divisor

(related to Lemma: Generalized Euclidean Lemma)

Let \(p\) be a prime number dividing a product of prime numbers $n=\prod_{i=1}^\rho p_i.$ Then $p$ equals at least one of these prime numbers, i.e. $p=p_i$ for at least one $i\in\{1,\ldots,\rho\}.$

Proofs: 1


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References

Bibliography

  1. Landau, Edmund: "Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927