Problem 1

Number Theory Level 2

How many ordered pairs ( x ; y ) (x;y) of non-zero positive integers exists to: 7 x + 3 y = 80 7x+3y=80 ?


The answer is 4.

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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1 solution

Aaaaa Bbbbb
Jul 9, 2014

It is easy to get y by: y = 80 − 7 x 3 ⇒ x m o d ( 3 ) = 2 ⇒ x = 2 , 5 , 8 , 11 ⇒ A N S = 4 y=\frac{80-7x}{3} \Rightarrow x \mod(3)=2 \Rightarrow x=2,5,8,11\Rightarrow ANS=\boxed{4}

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