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Add to a Square Number

Submitted By:shenqiang
Fun:** (1.78)
Difficulty:*** (2.85)

A, B and C are positive integers such that 3^A+5^B+7^C is a square number.

What is the minimum value of this square number?

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Comments on this teaser

Posted by jhosek04/21/11
figured it out by trial and error but wondering if there is an explanation or mathematical formula that leads to the answer.

Posted by Karnage199307/24/11
Yes I too am wondering if there is a mathematical way to do this. I tried finding the derivative of the equation to get the minimum value that it would produce but (3^a)(ln3) + (5^b)(ln5) + (7^c)(ln7) never equals 0. Is this question truly guess and check? :(


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