A Medley of Mathematical Enigmas, Vol I


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If you'd like to excercise yor mathematical skills, try out my problems..

1. 550661dd300aeb91e12b03abf645c41.gif

Here's a simple one which only requires a bit of mathematical manipulation.. 

A, B, C are positive integers.

2. Find all angles θ in [0, 2π) for which
sin θ + cos θ + tan θ + cot θ + sec θ + csc θ = 6.4

3. A substuition will take you far here..

If  53b07e03ff33966d587bda9139c6661.gif  then  b0a02fa1b281457ddd057e0f896c981.gif  = x.

Find x.

(Hint: Use a bit of complex-mathematical trickery.)

4. Prove  $(1). \ \ \sum_{d|n} \sigma(d) \varphi \left(\frac{n}{k} \right) = n \tau(n)$

Hint: Use the fact that  $$\sum_{d|n}\varphi(d)=n$$.

Good luck, mathematical neophytes and adept analyzers!

Edited by IntegrationNation
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1 minute ago, Agent P said:

I don't know which software you're copying these from, but it's formatted horribly, the first question is almost unreadable.

It's because it's not meant to work on dark theme, but yeah. I changed my theme just now and it's pretty good now. Except for that squashed image in the Hint of No. 4.

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Just now, Master Flap said:

It's because it's not meant to work on dark theme, but yeah. I changed my theme just now and it's pretty good now. Except for that squashed image in the Hint of No. 4.

off topic, but how do you change the theme with the shortcut at the bottom of the page missing?

 

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5 hours ago, Master Flap said:

It's missing? I can still see it on desktop. 

Yeah, it's only visible to staff members; I can confirm I can't see it.. and I'm copying my images from a program that generates LaTeX.. which apparently is not all too compatible with dark mode.

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