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A Difference of Powers (Posted on 2024-07-31)

What is the smallest possible value of |36^m – 25ⁿ|, where m, n are positive integers?

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 3.0000 (1 votes)

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Easy (spoiler)

Comment 1 of 1

(36^m - 25^n) = (6^m - 5^n)*(6^m + 5^n)

The first factor can never be 0 and the second factor has a minimum value of 11, when m = n = 1.

So the minimum value is 11, when m = n = 1.

Posted by Steve Herman on 2024-07-31 11:59:28

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