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Prove that 10^(3n)+1 cannot be represented as a sum of the cubes of two integers

Appreciate thanks. Inbox would be helpful !
2. Hello, I've moved this to maths study help for you.
3. (Original post by Lauren_ellams)

Prove that 10^(3n)+1 cannot be represented as a sum of the cubes of two integers

Appreciate thanks. Inbox would be helpful !
Take so: . Did you mean ?
4. (Original post by Lauren_ellams)

Prove that 10^(3n)+1 cannot be represented as a sum of the cubes of two integers

Appreciate thanks. Inbox would be helpful !
10^(3n) + 1 = (10^n)^3 + 1^3, so it can be represented as the sum of two cubes.
The question is wrong.
5. (Original post by Zacken)
Take so: . Did you mean ?
yeah I did mean 10^(3n+1) my teacher gave the wrong question. could you give me a full explanation as it is worth 15 marks and I have no idea what to do!
6. (Original post by Lauren_ellams)
yeah I did mean 10^(3n+1) my teacher gave the wrong question. could you give me a full explanation as it is worth 15 marks and I have no idea what to do!
Work :

What are cubes , hence what are sums of two cubes are they ever ?
7. i don't know it doesn't say that is the question:/
8. (Original post by Lauren_ellams)
i don't know it doesn't say that is the question:/
What?
9. (Original post by Lauren_ellams)
i don't know it doesn't say that is the question:/
First of all, do you understand modular arithmetic?
10. (Original post by HapaxOromenon)
First of all, do you understand modular arithmetic?
yeah but it is so confusing. it has to be proven algebraically
11. (Original post by Lauren_ellams)
yeah but it is so confusing. it has to be proven algebraically
Read this: https://nrich.maths.org/4350 to understand modular arithmetic before going any further.
12. (Original post by Zacken)
What?
I don't understand the question, can you please show me the answer???
13. (Original post by Lauren_ellams)
I don't understand the question, can you please show me the answer???
It's a proof... there is no "answer".
14. the proof then
15. (Original post by Lauren_ellams)
the proof then
I've given you the outline, have you bothered reading it?
16. yeah but I don't understand
17. (Original post by Lauren_ellams)
yeah but I don't understand
What part don't you understand?
18. (Original post by Zacken)
What part don't you understand?
all of it
19. (Original post by Zacken)
What part don't you understand?
(Original post by Lauren_ellams)
all of it
this has been a very amusing thread

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