Base = Power

Number Theory Level 1

Consider two positive integers a a and b b which are such that a a b b a^a b^b is divisible by 2000 2000 . Find the least possible value of the product of a b . ab.


The answer is 10.

Vishal S by Vishal S , 21, India

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1 solution

Nayanmoni Baishya
Dec 10, 2014

2000=2^4x5^3. Therefore, least value of ab=2x5=10

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The question states (a^a)(b^b), from your answer, a^a≠2^4.. a is 2 and 4 at the same time..same goes to value of b.. Care to explain?

Razik Ridzuan - 6 years, 6 months ago

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My mistake. As 2000=4^2x5^3,which is divisible by 2000. So, definitely 4^4x5^5 is also divisible by 2000. Hence, answer should have been 4x5=20.

Nayanmoni Baishya - 6 years, 6 months ago

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