Estimating Prime Power Sums

Number theory is a field that has, for me, always held a special kind of magic. There is something about reading an elegant proof that sticks with me, gives me a certain feeling of gratification like the sensation experienced at the conclusion of a mystery novel. I have always believed that the objective of any mystery is to figure it all out before the grand reveal, to make the leaps of intuition before Sherlock Holmes. It is exactly that desire to investigate that compels me to study numbers. In number theory, when proving a theorem, you start with a problem, uncover clues, try out possibilities and Eureka! you’ve constructed a solution; case closed!

• Mathematics