Heron triangle and rhombus pairs with a common area and a common perimeter - Yong Zhang and Jinyao Peng

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    Heron triangle and rhombus pairs with a common area and a common perimeter - Yong Zhang and Jinyao Peng

    By Fermat's method, we show that there are infinitely many Heron triangle and θ-integral rhombus pairs with a common area and a common perimeter. Moreover, we prove that there does not exist any integral isosceles triangle and θ-integral rhombus pairs with a common area and a common perimeter.

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