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Find the largest value of a^b such that the positive integers a, b>1 satisfy a^b b^a+a^b+b^a=5329 .

Correct answer

81

Step-by-step solution

aligned & (a^b+1 ) (b^a+1 )=5330=2 5 13 41 & a^b=81=3^4 and b^a=64=4^3 aligned Or a^b=64=4^3 and b^a=81=3^4 a^b=81

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