Find All Possible Values - a Problem of Divisors | Number Theory | Viewer Suggested Problem

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This is a nice number theory problem sent in by a viewer.

b, c and d are the three smallest positive divisors of n, not equal to 1.
Also, n = b⁴ + c³ + d² + 9.
Can you find all possible values of n?

Did you solve it?
Let me know in the comments how you solved this problem. I’d love to hear about it!

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Maths videos by Giuliano Grasso - mathematics graduate from the University of East Anglia.

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Just want to add, at 0:18 I should have made it clearer that b must also be odd.

And at 1:07, d^2 is just 1 mod 4.

GGMaths

nice i like this problem because it involves divisors, never seen in this channel.

timetraveller

I remember that on a turkish contest "Antalya Math Olympiad" this problem was featured either 2017 or 2018. Nice solution btw !

asmocak

Do you have any video for mod equations??
Anyway, it's

samihaafsaraibnat

Yay ! The reason why I like problems involving divisors is because they use more common sense than Number Theory 😁
And your solution was very ingenious ! I liked it ! And once again thanks for mentioning me in the video, lol 😂

srijanbhowmick

Let n be a positive integer. Show that any number greater than n⁴/16 can be written in at most one way as the product of two of its divisors having difference not exceeding n.

(1998 St. Petersburg City Mathematical Olympiad)

Please solve this one on your channel .
Thanks.

TechToppers

2:29 "...plus 2p all squared..." but you write 8p^2. This doesn't affect the result, but it is a weird typo.

themathhatter

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