A Lateral Maths Puzzle

Apr 2012
263
107
Erewhon
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)
$2^8,\ 2^6.\ 2^5$

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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Feb 2015
2,255
510
Ottawa Ontario
Hint: a^3 + b^4 = c^5 = 976,562,500,000