Problem
NT-B1-M09-P004 A Prime Power
#4
★☆☆☆☆ Level 1 of 5
Prove that \(p^a\), where \(p\) is prime, has exactly \(a+1\) positive divisors.
Which powers of \(p\) can divide \(p^a\)?
Every positive divisor of \(p^a\) has the form \(p^k\), where \(k=0,1,\ldots,a\). There are \(a+1\) choices for \(k\). Hence there are \(a+1\) divisors.
Fundamental part of the general formula.