the past; yesterday; dusk

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This is the long-awaited Math Jester challenge for Fall of 2021. It is available as a PDF in the usual location, but it is also reproduced below in HTML. Enjoy!

Complete as many of the following problems as you can. You may use a calculator or Unix terminal for help with calculations, but show your work! Partial credit will be awarded for good reasoning.

Consider $\sqrt{612}$. Your mission, should you choose to accept it, is to convert this expression into $\sqrt{M^{2}N}$, where

*M*and*N*are integers. What is the largest value of*M*that satisfies this equation? What is the corresponding value of*N*? [2 points]

Hint: if you do this correctly,*N*will be an example of a*squarefree*^{[1]}factor of 612. What does this mean? How can you apply it?Now consider $\sqrt[3]{17000}$. Convert

*this*expression into $\sqrt[3]{M^{3}N}$, where*M*and*N*are integers. What is the largest value of*M*that satisfies this equation? What is its corresponding value of*N*? [4 points]

Hint: If you do this correctly,*N*is a*cubefree*^{[2]}factor of 17000. What does this tell you?Consider $\sqrt[5]{9143008}$. Convert this expression into $\sqrt[5]{M^{5}N}$, where

*M*and*N*are integers. What is the largest value of*M*that satisfies this equation? What is its corresponding value of*N*? [4 points]Now consider $\sqrt[6]{1927458368}$. Then use the strategies or patterns presented above in order to show that this expression is equal to $\sqrt[3]{ \sqrt[2]{1927458368}}$. Why do you think this is? Can you generalize this fact to a number other than 1927458368? [5 points]

Is this problem interesting? Why or why not? [3 points]

Weisstein, Eric W. “Squarefree.” From MathWorld – A Wolfram Web Resource. https://mathworld.wolfram.com/Squarefree.html

—. “Cubefree.” From MathWorld – A Wolfram Web Resource. https://mathworld.wolfram.com/Cubefree.html

perhaps; sometimes; "or"

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island

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-- Marie Kondo

Consider Discord (the chatting / social media platform).

In the days when I used to check Discord, I had regular access to people who had shared interests with me -- interests such as computer programming, science, politics, philosophy, Korean culture, music, and so forth.

It became typical for me to log into Discord and have a nearly-constant smile on my face as I reviewed the notifications that I had missed over the previous day (or week, or month, etc.). I would scroll through these, catching up on messages and replying to the people who were often wondering where I'd been, and the topics would often be about narrow, shared interests and inside jokes.

"And somewhere he was laughing, in a white-painted loft, distant fingers caressing the deck, tears of release streaking his face."

-- William Gibson,Neuromancer

By contrast, consider Facebook.

When I used to log into Facebook, I would be presented with one large post at the top of my feed that would immediately incite rage, jealousy, or shock, within a fraction of a second. It would be a post of somebody boasting about getting a new job, or sharing an academic achievement, or starting a serious relationship, or getting married, or something equally life-changing. Most of the time, I found myself experiencing an immediate wave of envy, simply because the thing that they had achieved was something that I had *wished* I could have achieved, and in some cases, it was something that I had worked hard for. But over time, I made another discovery: even when the thing being boasted was an accomplishment that *I had also achieved*, I still had a (albeit somewhat dulled) negative feeling arise within me. I could not help but think, quite consciously, that this kind of achievement -- say, a graduation celebration, or a job offer -- should not be something that one publicly boasts about. It is basically a display of show-offiness.

"A superior man is modest in his speech but exceeds in his actions."

-- Confucius

Eventually, my only reason for checking Facebook became communicating with a select few people, who used Facebook Messenger as a primary chat application (I refuse to download such an app, and the reasons behind that could fill a whole separate article; I will add them later). There was a time when I would attempt to use a custom program to check my Facebook messages without logging in to Facebook, but this had its own deficiencies.

Therefore, I decided to stop checking Facebook altogether, and I found myself infinitely more happy because of it. (Mind you, I do not consider myself a happy person, but based on the consistency of my experience, I do rest assured that I'd be even more unhappy had I continued to check Facebook.)

The moral of the story being, I would encourage all of you reading this to reflect critically on the emotions that your software is making you feel. Does it inspire amusement, pleasure, and meaning? Or alternatively: is it inciting envy, rage, and pain?

I happen to know I am not the only one who experiences these feelings when checking Facebook. As a matter of fact, it's been shown that Facebook has a history of manipulating its users and rewards posts that incite outrage. For more on this, I recommend the film *The Social Dilemma* and Tristan Harris' other work.

But in the last three months, I have *also* stopped checking Discord -- but this is for a different set of reasons that perhaps deserve their own separate post.

If I have since stopped checking both of these sites, you may reasonably wonder, what do I do with my time?

Well, I have since taken up book-reading as an activity to replace checking social media. Instead of short, punchy, sentence-long posts, you get the benefit of more lengthy, poetic, carefully-crafted passages -- in other words, I am rediscovering the forgotten world of slow-paced, thought-provoking storylines that I had largely left behind in 2016.

I recommend you try experiments like ``not checking my favorite social media site for 30 days'' and so forth. These experiments can be enlightening and bring more variety and depth of insight into one's life.

And in the meantime, feel free to follow the RSS feed for the math jester.

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eat; meal; food

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Achievement; merit; good result

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