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Enumeration

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The Möbius Function

29th October 2018 OldTrout 2281 Comments

The Möbius function is denoted by , where is the Greek letter mu. Depending on the factorisation of , the function takes the values . The last says that if is even, then and if [more…]

Hobbies

Euler’s Totient Function

6th August 2018 OldTrout 1964 Comments

Euler’s totient function counts the number of positive integers up to that are relatively prime to , where is considered to be relatively prime to all .  These numbers are called the totatives of . [more…]

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Elsewhere on GP

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    As I get older I seem to have frequent hazy days, foggy days where I’m not sure if this is reality any longer or some surreal, drug induced sleep. Picture yourself in a boat on [more...]
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    The (Postwar) Fall of France, Part Two

    29th October 2020 3892 Comments
    The black and beur (French-Arab) communities have always had complicated ties with France. The early waves of European immigrants — the Italians, the Spanish, the Poles — came from proud, independent peer cultures, and the [more...]
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    Nothing true is popular. One of the most disturbing revelations an individual human can receive is the fact that the majority are not always right. This statement might appear to be self evident, but if [more...]
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    Berne is the capital of Switzerland and enjoys a modern-day population of about 130,000. The old part of the city is contained within a bend in the river Aare which, along this part of its [more...]
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    I Learned About Flying From That Part Two

    30th November 2017 2482 Comments
    It was another hot morning in Fremantle, Western Australia in early January. Forecast for 36 degrees Celsius, 97 in old money. “Gonna be a scorcher, Geek-o!”, said my benevolent host and long-time friend Mike, whom [more...]

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