Aira's Problem

4000 a b × b a \large 4000 \mid a^b \times b^a

Let a a and b b be two positive integers such that a b × b a { a }^{ b }\times { b }^{ a } is divisible by 4000. Find the least value of the product of a a and b b .


The answer is 20.

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1 solution

Hana Wehbi
Mar 13, 2017

4000 = 2 5 × 5 3 4000=2^5\times 5^3 So the least product would be 2 2 × 5 = 20 2^2\times 5=20

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