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Fido Johnson (@JohnsonFido) profile picture

Fido Johnson

@JohnsonFido

Number theorist.

 United Kingdom
Joined December 2016
  • Tweets7.6K
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Photo by Fido Johnson (@JohnsonFido)Photo by Fido Johnson (@JohnsonFido)Photo by Fido Johnson (@JohnsonFido)Photo by Fido Johnson (@JohnsonFido)Photo by Fido Johnson (@JohnsonFido)Photo by Fido Johnson (@JohnsonFido)Photo by Fido Johnson (@JohnsonFido)Photo by Fido Johnson (@JohnsonFido)Photo by Fido Johnson (@JohnsonFido)Photo by Fido Johnson (@JohnsonFido)
Replying to @Daily_Epsilon @GwoMaths
Today we enjoy the famous MARKOV EQUATION x² + y² + z² = 3xyz This simple equation results in some utterly fabulous number theory! Fancy some fun? Come take a peek. [Thread…]
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I would be astounded if “almost everyone” were to answer 1/3.
Tradermath (@Tradermath_org) profile pictureTradermath
@Tradermath_orgSep 13
Three fair coins are flipped. You are told at least one came up heads. What is the probability that exactly one did? Almost everyone answers 1/3. It is not 1/3. This one gets asked in trading interviews for exactly that reason.

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A fun modular arithmetic puzzle.
Fido Johnson (@JohnsonFido) profile pictureFido Johnson@JohnsonFidoMay 5
Replying to @geoclidean
Nice one! Note that mod 60: (i) 34n generates all evens (ii) 34n + 47 generates all odds (ii) 47+47 ≡ 34 So any second-hand sequence includes at least one of 34n or 34(n-1)+47, for n=0 to 29. Set n=24 to show that any sequence must contain 36 or 49 ✅
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Fido Johnson retweeted
Fido Johnson (@JohnsonFido) profile picture
Fido Johnson@JohnsonFidoApr 15
Replying to @JohnsonFido @barrygoldman1 @CPierre67 @chris_juravich @neurodocente
Here is a proof that the maximum sequence length is indeed n=9. Inter alia it also demonstrates that n=9 is only achievable with f(2) and f(3) both equal to 3, as per @barrygoldman1’s example.
Image from Fido Johnson (@JohnsonFido)
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Using a Lucas sequence to solve a common Twitter maths puzzle. Hopefully of interest @chris_juravich
Image from Fido Johnson (@JohnsonFido)
Image from Fido Johnson (@JohnsonFido)
Image from Fido Johnson (@JohnsonFido)
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This related post may also be of interest. teapawt.net/daily_epsilon/status/1…
Your Daily Epsilon of Math (@Daily_Epsilon) profile pictureYour Daily Epsilon of Math@Daily_Epsilon15 Jul 2021
Replying to @Daily_Epsilon
Yesterday's problem with solution by @JohnsonFido -- way more to this one than it first appears! Thank you so much, Fido!
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Some fabulous elementary number theory questions 👇🏻
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Replying to @Daily_Epsilon
🥇🥈🥉 THREE SOLUTIONS 🥇🥈🥉 Here are three ways to solve today’s question: however, two are perfectly valid, but one most definitely is not! But which are the ✅ ✅ and which is the 🤡?
Image from Fido Johnson (@JohnsonFido)
Image from Fido Johnson (@JohnsonFido)
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Fido Johnson retweeted
Fido Johnson (@JohnsonFido) profile picture
Fido Johnson@JohnsonFido3 Dec 2022
Replying to @Daily_Epsilon
So much beautiful mathematics in today’s question that I couldn’t resist doing a solution. Well, three solutions! I did this quickly over breakfast, so happy to take questions or corrections 😀
Image from Fido Johnson (@JohnsonFido)
Image from Fido Johnson (@JohnsonFido)
Image from Fido Johnson (@JohnsonFido)
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Here is a solution to yesterday's #dailymaths problem from Number Theory superstar @JohnsonFido. Thanks Fido!
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Here is a solution to yesterday's #dailymaths problem from frequent contributor, Professor @JohnsonFido. She included a proof of Zeckendorf’s Theorem, just because of course she did! Thanks Fido!
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Image from Your Daily Epsilon of Math (@Daily_Epsilon)
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Replying to @juanjgpt @mathisstillfun
Rather than repeating ‘no that’s not valid’ I thought I’d set out a formal proof. I do not think that a divisibility testing approach works. This is the simplest way that I can see to do it.
Image from Fido Johnson (@JohnsonFido)
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Here is a thorough explanation and solution to yesterday's #dailymaths problem, which is actually a pretty famous math problem, from professor Fido. Thanks @JohnsonFido!
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Here is Professor Fido's promised followup note to yesterday's #dailymaths problem. Thanks for the lesson @JohnsonFido!
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Image from Your Daily Epsilon of Math (@Daily_Epsilon)
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Here is a solution to yesterday's #dailymaths problem from our favorite number theorist, @JohnsonFido. Be sure to read her followup post where she proves "the most significant artefact in number theory and possibly all of mathematics" (her words but I'm not arguing). Thanks Fido!
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Here is a solution to yesterday's #dailymaths problem from the inimitable @JohnsonFido. Thanks Fido!
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Here is a solution to yesterday's #dailymaths problem, courtesy of the one, the only, the great @JohnsonFido. :) Thanks Fido!
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Here is a solution to yesterday's #dailymaths problem from Professor Fido. Thanks @JohnsonFido!
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Here is a solution to yesterday's #dailymaths problem from Professor Fido. Thanks @JohnsonFido!
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Here is a solution to yesterday's #dailymaths problem from Professor Fido. Thanks @JohnsonFido!
Image from Your Daily Epsilon of Math (@Daily_Epsilon)
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Here is a solution to yesterday's #dailymaths problem from Professor Fido. Thanks @JohnsonFido!
Image from Your Daily Epsilon of Math (@Daily_Epsilon)
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