Sunday, February 03, 2013
\(\varphi(1) = 1\)
But why ? Observe that
\( \varphi(n) \) is equal to the number of integers between \(0\) and \(n-1\) that are relatively prime to \(n\).Trivially, \(gcd(0,n) = n\) as \(n\) divides \(0\), but \(gcd(0,n) = 1\) only when \(n = 1\). In other words, zero is relatively prime to \(n\) only in the case when \(n = 1\). Therefore, zero only counts in \(\lvert \mathbb{Z_1} \rvert\). \(\Box\)
