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Thread: A Lateral Maths Puzzle

  1. #1
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    A Lateral Maths Puzzle

    Find any positive integers a, b, c such that a^3 + b^4 = c^5
    (a cubed plus b to the power 4 = c to the power 5)

    Taken from Mathematical Lateral Thinking Puzzles by Paul Sloane and Des MacHale


    A Lateral Maths Puzzle-mathlat.jpg
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  2. #2
    Senior Member zzephod's Avatar
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    Re: A Lateral Maths Puzzle

    Quote Originally Posted by PaulSloane View Post
    Find any positive integers a, b, c such that a^3 + b^4 = c^5
    (a cubed plus b to the power 4 = c to the power 5)
    Spoiler:

    $2^8,\ 2^6.\ 2^5$


    Extension:
    Is this solution unique? If not is there a solution with largest c?

    [if I remember I will post the answer to the extension in a week or so]

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    Last edited by zzephod; Dec 3rd 2016 at 12:07 PM.
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  3. #3
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    Re: A Lateral Maths Puzzle

    Hint: a^3 + b^4 = c^5 = 976,562,500,000
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