Since there are infinitely many primes, what are the largest primes that we know of?The largest known primes are ones of...
Continue reading...number theory
Powers of Ten in Base Two and Five
Make two lists; one consists of all powers of 10 in base 2, and the other all powers of 10...
Continue reading...Toggling Light Switches
Imagine 100 light bulbs with light switches numbered 1 through 100, all in a row, all off. Suppose you do...
Continue reading...Sums of Reciprocal Powers
You have seen that the harmonic series diverges. What about the sum of reciprocal squares? In fact, they converge, and to something...
Continue reading...Sum of Cubes
The sum of cubes is just the square of the triangular numbers! 13 + 23 + … + n3 = (1 + 2 + … + n)2. And there...
Continue reading...Magic Squares, indeed!
Perhaps you’ve seen the magic square 8 1 6 3 5 7 4 9 2 which has the property that all rows,...
Continue reading...Pascal’s Triangle
Consider the triangle in Figure 1, called Pascal’s triangle. It consists of numbers where each entry is the sum of the...
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