Question

Encontre a diofantinasde 8x+y11=50

Answer 1

Olá Pelé.


Organizando e encontrando a equação que represente todas as soluções da equação diofantina.

$\mathsf{8x+11y=50}\\\\\mathsf{8x+0y\equiv~6~(mod~11)}\\\\\mathsf{\diagup\!\!\!\!2\cdot4x\equiv\diagup\!\!\!\!2\cdot3~(mod~11)}\\\\\mathsf{4x\equiv3~\cdot(3)~(mod~11)}\\\\\mathsf{12x\equiv9~(mod~11)}\\\\\mathsf{x\equiv~9~(mod~11)}\\\\\boxed{\mathsf{x=11k+9}}\\\\\\\mathsf{8\cdot(11k+9)+11y=50}\\\\\mathsf{88k+72+11y=50}\\\\\mathsf{11y=-88k-72+50}\\\\\mathsf{11y=-88k-22~\cdot\Big(\dfrac{1}{11}\Big)}\\\\\boxed{\mathsf{y=-8k-2}}$


Dúvidas? comente.