is this my new favorite number??

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[iWilburnYou]

13:34 Michael nonchalantly admitting to be the oldest recorded person by almost 200 years is crazy

10:52
Why is 1996 congruent to 0 mod 6?

[MothRay]

“Alexis Claude Clairaut (French pronunciation: [alɛksi klod klɛʁo]; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist.”

[aerglo]

Hey Michael
I just wanted to appreciate your videos and the efforts you are making. The problems you introduce are often very interesting.
Thanks

[petermayes]

I can follow the solution process. But I have absolutely no idea how somebody could set such a problem in the first place, without knowing how it is going to work out. Would love Michael to give some insights into how people set questions for Olympiads, competitions etc.

[gslpkoc]

Had no idea why you started doing modular arithmetic until the last few seconds!

[supratimsantra]

Sir wonderful discussion, it is like a thunderstorm in mind to get spark of motivation towards magic of mathematics, the top of all sciences

[davidgillies]

I have a hankering to write a bit of C or C++ code to evaluate this exactly. I'm not entirely sure how many digits it has but a quick bit of experimentation suggests 600 thousand or so, although possibly a LOT more because the partial products get very big around n = 1998/2 (similar to how the middle of a row of Pascal's triangle gets very big).

UPDATE: actually it's not all that big. The parentheses round the inner sum tame it quite well. It's 13186 digits.

[pietergeerkens]

At 11:07, note that 1996 is congruent 1 (mod 3) - just add the digits to see this, getting 1+9+9+6 = 25 and 2+5 = 7.

[tahirimathscienceonlinetea]

Hi micheal you deserved million thumbs up Excellent job

[qedmath]

Shifting the index was unnecessary and in fact slower than just using the formula for a geometric series, but nonetheless good demonstration on how to shift indexes in summations. Really nice video and problem!

[deebd]

If I'm not mistaken, m^1998 is 1 (mod 7) for any m, and therefor, when calculating mod 7, the inner sum can simply be replaced with n. But then I get as result that the total sum is 3 (mod 7) instead of 5 (mod 7). This would still prove that it can't be a perfect square, but where is my error?

[drssimonhottentot]

1996 is not divisable by 6, so not congruent 0 mod 6.

[doraemon]

Is that a reference to the 200-300 years of history missing?

[mskellyrlv]

You don't look a day over 300. 🙂 Every time my wife walks in while I'm watching one of your videos, she remarks "Oh, watching math porn again?" Yep!

[kkanden]

guys this is not the first time that michael hints at being 300 years old, he's trying to send a message

[mathhack]

simply Amazing. best thing to start the day with this Demo. .

[charleyhoward]

does the 666 at 16:55 mean anything to Micheal ??? Hmmm ??

[quazzydiscman]

What's your favorite number?

Me: 17

Michael Penn:

[Sunlessilver]

Hello love your vids. Is there anything interesting about an equation with infinite positive and negative powers set equal to 0. It would look like