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benjamin dickman @benjamindickman.bsky.social · 5h

yeah I saw some students looking at number theory propositions that were obviously false!

even something like "6n+1 is a multiple of 3" works with the inductive step but not the base case

... food for thought on our next exam or problem set 🤔🤔🤔

Reposted by benjamin dickman

benjamin dickman @benjamindickman.bsky.social · 1d

cc #iTeachMath ♾️!

Dave Kung @dtkung.bsky.social · 2d

Always fun to see the amazing people who win. Congrats to mathematician Lauren Williams on winning a MacArther genius grant!

www.macfound.org/fellows/clas...

Lauren K. Williams

Uncovering transformative connections between algebraic combinatorics and problems in other areas of math and physics.

www.macfound.org

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Reposted by benjamin dickman

benjamin dickman @benjamindickman.bsky.social · 1d

here are the inductive steps (abbreviated):

factor:
4^(n+1) + 2 = 4(4^n) + 2 = (3+1)4^n + 2
= 3(4^n) + (4^n + 2)

substitute:
2^(n+3) + 3^(2n+3) = 2(2^(n+2)) + 9(3^(2n+1))
= 2(7m - 3^(2n+1)) + 9(3^(2n+1))
= 7(2m + 3^(2n+1))

multiply:
5^n - 1 = 4m
5^(n+1) - 5 = 20m
5^(n+1) - 1 = 20m+4 = 4(5m+1)

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Reposted by benjamin dickman

benjamin dickman @benjamindickman.bsky.social · 1d

For all n ≥ 1, the following propositions are true:

1) 4^n + 2 is div. by 3
2) 2^(n+2) + 3^(2n+1) is div. by 7
3) 5^n - 1 is div. by 4
4) 2^n ≥ n+1

The first three were proved using methods referred to with the verbs: factor, substitute, and multiply; the last was proved by combining inequalities!

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benjamin dickman @benjamindickman.bsky.social · 8h

another #DesmosDemo for #iTeachMath & #MathSky!

check out the Emmy-award winning* show from Sara and Sean

—

*ok it hasn't won anything but it hasn't lost either!

Graph Time with Sara and Sean @graphtimesarasean.bsky.social · 12h

How we animate in Desmos, Episode 3 of Graph Time with Sara and Sean is here!

youtu.be/PtrHw9-AFWQ

How we animate in Desmos, Episode 3

YouTube video by Graph Time with Sara & Sean

youtu.be

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benjamin dickman @benjamindickman.bsky.social · 13h

I saw it. It was great. We were so young 🌱

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benjamin dickman @benjamindickman.bsky.social · 1d

‼️

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benjamin dickman @benjamindickman.bsky.social · 1d

s a m e Thursday #2solve

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benjamin dickman @benjamindickman.bsky.social · 1d

here are the inductive steps (abbreviated):

factor:
4^(n+1) + 2 = 4(4^n) + 2 = (3+1)4^n + 2
= 3(4^n) + (4^n + 2)

substitute:
2^(n+3) + 3^(2n+3) = 2(2^(n+2)) + 9(3^(2n+1))
= 2(7m - 3^(2n+1)) + 9(3^(2n+1))
= 7(2m + 3^(2n+1))

multiply:
5^n - 1 = 4m
5^(n+1) - 5 = 20m
5^(n+1) - 1 = 20m+4 = 4(5m+1)

1 2

benjamin dickman @benjamindickman.bsky.social · 1d

bonus note if you read this far:

I miswrote the second proposition (I lost a 2!) so ... good luck proving it as posted lol

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benjamin dickman @benjamindickman.bsky.social · 1d

For all n ≥ 1, the following propositions are true:

1) 4^n + 2 is div. by 3
2) 2^(n+2) + 3^(2n+1) is div. by 7
3) 5^n - 1 is div. by 4
4) 2^n ≥ n+1

The first three were proved using methods referred to with the verbs: factor, substitute, and multiply; the last was proved by combining inequalities!

1 1 2

benjamin dickman @benjamindickman.bsky.social · 1d

in #MathsToday: four different propositions, each proved by induction.

Fascinatingly, the first three (divisibility statements) were all proved using different but interchangeable methods.

The full statements from the image can be found below 👇🏻

see next post or tweet or whatever for the content of this image

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benjamin dickman @benjamindickman.bsky.social · 1d

cc #iTeachMath ♾️!

Dave Kung @dtkung.bsky.social · 2d

Always fun to see the amazing people who win. Congrats to mathematician Lauren Williams on winning a MacArther genius grant!

www.macfound.org/fellows/clas...

Lauren K. Williams

Uncovering transformative connections between algebraic combinatorics and problems in other areas of math and physics.

www.macfound.org

2 4

benjamin dickman @benjamindickman.bsky.social · 2d

twinning w Wed #2solve

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benjamin dickman @benjamindickman.bsky.social · 2d

my headers are cabin, body gentium book basic

benjamin dickman @benjamindickman.bsky.social · 2d

tbh this is worth it

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benjamin dickman @benjamindickman.bsky.social · 2d

uncommon

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benjamin dickman @benjamindickman.bsky.social · 2d

i read Who's Afraid of Gender (previous school year) and it was hard reading in multiple ways (sadly prescient; dense and overly fond of the word phantasm)

benjamin dickman @benjamindickman.bsky.social · 2d

day 2 of LinkedOut games:
still playing them when I first wake up instead of when I'm fully awake; still xcl on phone

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benjamin dickman @benjamindickman.bsky.social · 3d

as the good lord intended!!

yes, my initials are a nickname I sometimes use

and, correspondingly re: anagrams,

nickname BD = Ben Dickman

(capitalization held constant!)

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benjamin dickman @benjamindickman.bsky.social · 3d

great #2solve pairing today for this Tue solve!

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benjamin dickman @benjamindickman.bsky.social · 3d

totally agreed, xcl gotta be on ⌨️ and Zip Tango Queens on 📱

mixed on Sudoku, which isn't my strong suit

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benjamin dickman @benjamindickman.bsky.social · 3d

LinkedOut games dropping a public leaderboard [for connections] is going to shift my playing style from wake up [first thing in the morning, still half asleep] to blitz [wait until later, play fully awake]. not sure if this is an improvement!

PS: play #FiddleBrix for true 🔡 joy!!
www.fiddlebrix.com

screenshot of fiddlebrix.com landing page; a 5x5 board contains the letters in play, beneath it are the tiles ("brix") spelling out FiddleBrix; beneath that is the phrase "A colorful daily word puzzle"; at the bottom are two buttons to download (one for Apple and one for Android)

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benjamin dickman @benjamindickman.bsky.social · 4d

minimal #2solve for Monday 6 Oct 2025:

01001111 01010110 01000101 01010010 01000110 01001001 01010100 01010011 00100000 01010011 01001000 01000001 01010111 01001100

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benjamin dickman @benjamindickman.bsky.social · 5d

see also the account written up by Terry Tao on Mathstodon:
mathstodon.xyz/@tao/1153167...

Terence Tao (@[email protected])

An update on my previous post https://mathstodon.xyz/@tao/115306424727150237 regarding how I was able to use modern AI to help solve a MathOverflow problem. Superficially, this story favors the "you ...

mathstodon.xyz

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