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    • Thread Starter
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    sum of the digits of

    444,444,444,444,445^2 - 555,555,555,555,555^2

    sorry edited by accident
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    -111111111111111111111111111111

    MdSalih
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    that;'s not the sum of digits though :-)
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    The number is -11...1(14 digits) x 10^16
    So the sum of digits is 14
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    well done

    harder question
    what three digit number divides (2^32 + 1)?
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    (Original post by mik1w)
    well done

    harder question
    what three digit number divides (2^32 + 1)?
    641 divides F_5

    (c) Mr Euler
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    (Original post by mik1w)
    well done

    harder question
    what three digit number divides (2^32 + 1)?
    The more interesting question is how do we know that F_5 is divisible by 641?

    Answer:
    Let a=2^7, b=5, so that a - b^3 = 3, 1+ab-b^4=1+3b=2^4

    Therefore,

    2^(2^5) + 1 = (2a)^4 + 1 = (1 + ab - b^4)a^4 + 1 = (1+ab)a^4 + 1 - (a^4)(b^4), and this must be divisible by 1+ab=2^4 + 5^4=641
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    (Original post by MdSalih)
    -111111111111111111111111111111

    MdSalih
    Just wondering why imperial is your first choice, not Cambridge?
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    i am wondering as well
 
 
 
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