Just divide

Number Theory Level 3

When a natural number $x$ is divided by 5, the remainder is 2. When a natural number $y$ is divided by 5 the remainder is 4.The remainder is $z$ when $x+y$ is divided by 5. Find the value of $\dfrac{2z-5}{3}$ .

The answer is -1.

1 solution

Guilherme Niedu
Jul 7, 2016

$x = 2 \text{ (mod 5)}$

$y = 4 \text{ (mod 5)}$

Hence:

$(x+y) = 1 \text{ (mod 5)}$

(Because $4 + 2 = 6$ and $6 = 1 \text{ (mod 5)}$

So $z = 1$ and $\frac{2z-5}{3} = \fbox{-1}$

Just divide

The answer is -1.

1 solution

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