• anonymous
Find all solutions of the following linear congruence. $$3x\equiv2\mod7$$ First of all, we notice that $$(3,7)=1$$. Therefore, we will only have $$1$$ solution. We now need to obtain a solution of the linear, diophantine equation $$3x-7y=2$$. The Euclidean algorithm gives: $$7=3\cdot2+1$$, $$3=1\cdot3+0$$. Hence, $$7\cdot1-3\cdot2=1$$ and $$7\cdot2-3\cdot4=2$$. Therefore, a particular solution to the diophantine equation is $$x_0=-4$$, $$y_0=-2$$ and all solutions of the linear congruences are given by $$x\equiv-4\equiv3\mod7$$. Am I right?
Mathematics
• Stacey Warren - Expert brainly.com
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SOLVED
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