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1. ### Primitives triangle with smallest side an even number

So, there are two attacks to proof it, both of them assume that a and b are odds: 1) If a and b are odds, c can not be rational, contradicting the assumption that all are rationals and primitives. 2) If a and b are odds, c can not be even which makes the area of the triangle, d, not integer...
2. ### Primitives triangle with smallest side an even number

But this could be also applicable in any triangle, namely, the area of any triangle can not be a positive integer unless one of its sides is an even number. But in the right triangle whose a, b are odd, c can not be even ( because c2 is not divisible by 4). This means in order for the area of...
3. ### Primitives triangle with smallest side an even number

If both a&b are odd, d can not be integer. So, d can not be integer except when one of a&b is even which completes the proof without need for Pythagoras theorem.
4. ### Primitives triangle with smallest side an even number

Ok, I tried that, if a, b, c are co-primes, then the area of the triangle is: $$area=\frac{1}{2}ab=d$$ $$ab=2d$$ which means one of a or b must be even.
5. ### Primitives triangle with smallest side an even number

Homework Statement Prove that if a right triangle has all sides rational and primitives (co-primes), then one of the smaller side must be even number. Homework Equations For a right triangle (a,b,c) with c is the hypotenuse. $$a^2+b^2=c^2$$ The Attempt at a Solution In order to create a...