Fermat told me this fraction was important.

You're on the margin now Chalk, I've got you right where I want you! There's no escape! well...unless you exclude the vents, that small door and the gate around back...OTHERWISE....there's no escape...hey!...where'd he go!?

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[luisaleman]

This should have been Fermat's little quotient, since it arises from Fermat's little theorem.

[buddhabuck]

Another possible extension would be to Euler's little quotient: What numbers n make (2^phi(n)-1)/n a perfect square?

[goodplacetostop]

13:17 *insert joke about Fermat’s margin note*

[Alan-zftt]

Brilliant! Love the use of decomposition and deductions

[MathOrient]

Absolutely fascinating! This video on Fermat's little quotient blew my mind. I never realized the intricate connections between this concept and Fermat's little theorem

[udic]

8:28 if n=1 => b^2=1 => b=1 => n=1? why the calculation? if n=1 then p=3. no need to find b.

[GandalfTheWise]

I tossed the generalized version into Mathematica for a few smaller integers. Interestingly, there are other solutions where a>2. (a, p) = (3, 2) (3, 5) (7, 3) (9, 2) (19, 2) (26, 3) (33, 2). The ones where p=2 form a regular sequence of 3, 9, 19, 33, 51, 73... where the difference between terms is 4n+2 so x[1]=3, x[n+1]=x[n]+4n+2. The first ones where p=3 are 2, 7, 26, 97, 362, 1351, 5042... Rather interestingly, p=5 only has a single solution for a<100, 000. This is obviously not a proof, but it appears there are an infinite number of (a, 2) and maybe (a, 3) whereas (a, 5) seems to have only a single solution or huge steps between a values. Given the "polynomial" in the equation is of the form a^(p-1)-1, it makes me wonder if there only being closed form solutions for roots for polynomials of quartic degree or less might play a role here. Anyway, a few numeric experiments to shed some light on the more general case.

[manucitomx]

A lot can come out from a little quotient, but no gnarliness.
Thank you, professor.

[mcbeaulieu]

Found 3 and 7 from the problem's writing yay lol

[pierreabbat]

What if you use other numbers than 2 as a?

[tinnguyen]

What values of a makes the quotient a perfect cube and so on?

[PhoenixInfeno]

Man, if you're gonna throw in a shout out to cryptography, should have gotten NordVPN to sponsor the video!

[Unidentifying]

Can someone help me solve ? ∫ e^(- x^2/(2+ix)) * e^(- x^2/(2-ix)) dx from -inf to inf

[parajulisugam]

Can anyone help me? I am a math olympian and I dont have money to buy laptop? I will give you 10x in the future?

[yedidiapery]

tbh i like your videos but i'm not subscribed because you upload so many videos, and i only watch a few of those