Numeral systems

[Guest]

Hey, so I study in a math high-school and everyone in our class is required to gather and explain to the others 10 problems in a more specific field in maths, like trigonometry or stuff like "prove that 5^n + 7^n is always divided by 11 " (Of course, this is probably not true, I just made it up )
So I got to pick last and there was pretty much nothing good left.I was handed Numeral systems.
I'm in 10th grade, and honestly, I can't think of any examples of such problems, that would require converting to another numeral system, other than the plain "convert 18543 into binary numeral system", but given my grade, I don't think I should turn up with such "problems"
So if you can think of any or give me a link, I'd be really thankful (Provision of the solutions is recommended )

[Math Tutor]

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