Tricky Square Number Problem! help!

Snic1123

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What is the smallest square number that can be formed by adding the squares of two smaller numbers?
 
25=9+16

Is the smallest using natural numbers.
because (3,4,5) is the smallest right triangle

i.e. The minimum Pythagorean triple.
 
Last edited:
25=9+16

Is the smallest using natural numbers.
because (3,4,5) is the smallest right triangle

i.e. The minimum Pythagorean triple.

1 more question. What about if negative exponents could be used? So not just using natural numbers?
 
What is the smallest square number that can be formed by adding the squares of two smaller numbers?

Hi Snic,

By definition, a "square number" is an integer which is also the square of an integer. Therefore, the answer must be a positive integer. (We can't pick zero because it's impossible to sum squares of a pair of numbers each smaller than zero to get a total of zero.)

However, the question does not specify any particular category for the two smaller numbers; therefore, the two smaller numbers may each be any Real number.

Since we seem to be giving away answers today, I'll post my answer. I say that the answer is 1.

\(\displaystyle \left(\dfrac{1}{2}\right)^{2} + \left(\dfrac{\sqrt{3}}{2}\right)^{2} = 1\)

In other words, the two smaller numbers are 0.5 and 0.8660254 (rounded).

What do you think of my interpretation?

Cheers :)
 
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