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    will someone please help me with this question for university?

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

    Appreciate thanks. Inbox would be helpful !
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    Hello, I've moved this to maths study help for you.
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    (Original post by Lauren_ellams)
    will someone please help me with this question for university?

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

    Appreciate thanks. Inbox would be helpful !
    Take n=1, b=1, a=10 so: 10^3 + 1 = a^3 + b^3. Did you mean 10^{3n+1}?
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    (Original post by Lauren_ellams)
    will someone please help me with this question for university?

    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.
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    (Original post by Zacken)
    Take n=1, b=1, a=10 so: 10^3 + 1 = a^3 + b^3. Did you mean 10^{3n+1}?
    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!
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    (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 \pmod{7}:

    10^{3n+1} \equiv 3^{3n+1} \pmod{7} \equiv 3 \times 27^n \pmod{7} \equiv (-1)^n \times 3 \pmod{7} \equiv \pm 3 \pmod{7}

    What are cubes \pmod{7}, hence what are sums of two cubes \pmod{7} are they ever \pm 3?
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    i don't know it doesn't say that is the question:/
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    (Original post by Lauren_ellams)
    i don't know it doesn't say that is the question:/
    What?
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    (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?
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    (Original post by HapaxOromenon)
    First of all, do you understand modular arithmetic?
    yeah but it is so confusing. it has to be proven algebraically
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    (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.
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    (Original post by Zacken)
    What?
    I don't understand the question, can you please show me the answer???
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    (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".
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    the proof then
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    (Original post by Lauren_ellams)
    the proof then
    I've given you the outline, have you bothered reading it?
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    yeah but I don't understand
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    (Original post by Lauren_ellams)
    yeah but I don't understand
    What part don't you understand?
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    (Original post by Zacken)
    What part don't you understand?
    all of it
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    (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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