# Solution 91: The Last Three Digits of a Phi-Exponent Tower

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**Published on May 15, 2019**- For a quick computational overview of Euler's Totient Theorem and Chinese Remainder Theorem: usclip.net/video/vv57_W5HMTg/video.html

Congratulations to Jaleb, Minh Cong Nguyen, Kevin Lu, Serengeti Ghasa, Arghyadeep Chatterjee, Nicolas Nauli, Midas Schonewille, and Mokou Fujiwara for successfully solving this math challenge question! Juju Mas was the first person to solve the question.

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For more Weekly Math Challenges:

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ShakeitpiggyMonth agoWow. I did it by finding patterns in the last 2-3 digits of powers of 6 and powers of 8. I still arrived at the right answer though.'

Jan Von SchreibeMonth agoWhat does it mean that a number _p_ is relatively prime to another number _n_ ?

Is is that _p_ does not divide _n_ ?

Alberto ZordanMonth ago^{+1}No. Two numbers are co-prime (relatively prime to each other) if they do not share any common factors, or equivalently if their greatest common divisor is 1.

Dragon95161Month ago^{+1}Really great video, how do you come up with these awesome maths questions???

adandapMonth agoI was frustratingly close to that. Of your N steps, I had N-2 of them written down but couldn't quite pull it all together. I'll work through it carefully and hopefully the next time Euler raises his head I'll get there.

KRISHNA KAMALAKANNANMonth agoWhen are you releasing the solution for this week's video?

LetsSolveMathProblemsMonth agoI will try to release it by this Thursday at the latest.

Sitanshu ChaudharyMonth agoBut how to take mod 1000 by u 1:30

magnifecentMonth agoSpeech 100

Benjamin WangMonth agonot sure what you mean by that :O

Zamir CMonth ago^{+12}I hope this video helps me to get a GF and stop watching ecchi animes

The Maverick!Month ago^{+2}@Zain Majumder I did that. No luck.

Zain MajumderMonth ago^{+2}i wish you luck, maybe you'll get girls by demonstrating your mathematical prowess

The Cold TomatoMonth ago^{+2}Will you go over the 2019 FRQ problems for the AP Calculus BC test when it is released?

LetsSolveMathProblems29 days ago@Smokie Bear 🔴🔵 *Edit: After much debate, I decided to not upload AP FRQ videos for this year, mainly because I believe I cannot post a series of explanation that is of a significantly higher quality than those already posted. If you are interested, turksvids has uploaded all solutions to AP Calclus AB/BC FRQ's from this year: usclip.net/user/turksvids

LetsSolveMathProblems29 days ago*Edit: After much debate, I decided to not upload AP FRQ videos for this year, mainly because I believe I cannot post a series of explanation that is of a significantly higher quality than those already posted. If you are interested, turksvids has uploaded all solutions to AP Calclus AB/BC FRQ's from this year: usclip.net/user/turksvids

The Cold TomatoMonth ago@Smokie Bear 🔴🔵 So did I

Smokie Bear 🔴🔵Month agoI’m so mad. I think I got all the multiple choice right but on ONE part of ONE free response I made ONE mistake cuz I just assumed that the question was asked in the same way as it was in the practice questions. NotLikeThis

LetsSolveMathProblemsMonth ago^{+4}I do plan to review AP Calculus AB and BC Free Response problems once they are released. Best of luck on your score if you took the exam today! =)