Une formule simple pour le $\operatorname{pgcd}(a,b)$

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Démontrez que :
$\displaystyle \operatorname{pgcd}(a,b)= 2\sum_{k=1}^{a}\left(\frac{1}{2}+\Big\lfloor k\frac{b}{a} \Big\rfloor- k\frac{b}{a}\right)= 2\sum_{k=1}^{b}\left(\frac{1}{2}+\Big\lfloor k\frac{a}{b} \Big\rfloor- k\frac{a}{b}\right).$

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Solution by mathman

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Appliquez le théorème de Pick à un triangle rectangle de cotés a et b

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