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Topic: Heron triangle (Read 1316 times) |
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Christine
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Heron triangle
« on: Apr 24th, 2014, 8:02pm » |
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a, b, c are the sides of Heronian triangle.
a and b are odd square numbers.
then GCD(a, b, c) = 1
is it always true? can you provide a counterexample?
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Christine
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Posts: 159
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Re: Heron triangle
« Reply #2 on: Apr 25th, 2014, 9:23am » |
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a,b,c are the sides of a Heronian triangle
two sides are square numbers:
a, b are odd squares: (25, 25, 30)
a is even, b is odd : (16, 25, 39)
can we find a Heronian triangle whose two sides are even square numbers?
Is it possible to find a primitive Heronian triangle in which each side is a square number?
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towr
wu::riddles Moderator
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Re: Heron triangle
« Reply #3 on: Apr 25th, 2014, 2:20pm » |
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on Apr 25th, 2014, 9:23am, Christine wrote:| can we find a Heronian triangle whose two sides are even square numbers? |
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Sure, just multiply by 4. It preserves squareness and adds evenness. So e.g. 100,100,120
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Wikipedia, Google, Mathworld, Integer sequence DB
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Christine
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Re: Heron triangle
« Reply #4 on: Apr 25th, 2014, 5:02pm » |
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can we find a Heronian triangle whose two sides are even square numbers?
I'm sorry, I forgot to mention a primitive Heronian triangle.
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dudiobugtron
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Re: Heron triangle
« Reply #5 on: May 22nd, 2014, 2:02pm » |
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on Apr 25th, 2014, 5:02pm, Christine wrote:| I'm sorry, I forgot to mention a primitive Heronian triangle. |
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You can't find a primitive Heronian triangle with both smaller sides even, because the hypotenuse will also be even.
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