Republic of Mathematics blog

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Fibonacci tricks from Palm Breeze CAFE

Posted by: Gary Ernest Davis on: November 17, 2010

Here’s the algebra: x x x x x x x More generally, if is the Fibonacci number, where , and is the sum of the Fibonacci numbers then   is an integer multiple of . For example, , and .

Ore numbers: how do they grow?

Posted by: Gary Ernest Davis on: November 15, 2010

An Ore number (also known as a harmonic divisor number) is a number whose harmonic mean of its divisors is an integer. The harmonic mean of a set of numbers is . When the are the whole number divisors of the number n, then we get the harmonic mean of the divisors of n. These […]