### Brain Teasers

# Add to a Square Number

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?

What is the minimum value of this square number?

### Answer

3^3+5^1+7^2=81.Hide Answer Show Answer

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## Comments

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

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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