I’ve delved deeply into divisiblity over the last few weeks, and am now examining properties of squares and sums of squares. I offer the following proof by induction (some algebraic manipulation is required as well). It is known that the sum of the squares of the first n natural numbers is equal to [( n… Continue reading Proof By Induction: Sum of the Squares of Natural Numbers
So I did go ahead and program a dynamically generated Sieve of Eratosthenes, but I just wanted to write a quick post about divisibility by 3 before I write a novel about the Sieve. Many of us know the trick for checking an integer’s divisibility by 3: just sum the digits and if the resulting… Continue reading Testing Divisibility by 3.