Here’s an interesting characterization of primes: Wilson’s Theorem. A number P is prime if and only if (P-1)! + 1...
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Divisibility by Seven
Everyone learns in grade school some simple tests for divisibility by small numbers such as 2, 3, 5, and 9....
Continue reading...Zero to the Zero Power
It is commonly taught that any number to the zero power is 1, and zero to any power is 0....
Continue reading...Pi Approximations
Pi is the ratio of the circumference of a circle to its diameter. It is known to be irrational and its decimal...
Continue reading...Formula for Primes?
Is there a nice cozy formula that will always spit out primes? Try this one: f(n) = n2 + n +...
Continue reading...Binary Card Trick
You put a deck of cards in your pocket, and invite anyone in the audience to call out a number between 1...
Continue reading...Wallis’ Formula
Here’s a fun formula for Pi involving an infinite product, known as Wallis’ Formula: (Pi/2) = (2*2)(4*4)(6*6)/(1*3)(3*5)(5*7) It is somewhat surprising that...
Continue reading...Kaprekar’s Constant
Take any four digit number (whose digits are not all identical), and do the following: Rearrange the string of digits...
Continue reading...Fibonacci Number Formula
The Fibonacci numbers are generated by setting F0 = 0, F1 = 1, and then using the recursive formulaFn = Fn-1 +...
Continue reading...Successive Differences of Powers
List the squares: 0, 1, 4, 9, 16, 25, 36, 49, … Then take their successive differences: 1, 3, 5,...
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