Problem
NT-B1-M06-P002 A Prime Divides a Square
#2
★☆☆☆☆ Level 1 of 5
Let \(p\) be prime. Prove that if \(p\mid a^2\), then \(p\mid a\).
Use Euclid's lemma for the product \(a\cdot a\).
Since \(a^2=a\cdot a\) and the prime \(p\) divides this product, Euclid's lemma gives that \(p\) divides at least one factor. Both factors are \(a\), so \(p\mid a\).
Can be connected to uniqueness of prime factorisation.