# modulus

#### jacks

##### Well-known member
If $$y = \mid x \mid+\mid x-1 \mid+\mid x-3 \mid+\mid x-6 \mid+...........+\mid x-5151 \mid$$

and $$m =$$ no. of terms in the expression $$y$$

and $$n =$$ no. of integers for which $$y$$ has min. value

Then $$\displaystyle\frac{m+n-18}{10} =$$

#### CaptainBlack

##### Well-known member
If $$y = \mid x \mid+\mid x-1 \mid+\mid x-3 \mid+\mid x-6 \mid+...........+\mid x-5151 \mid$$

and $$m =$$ no. of terms in the expression $$y$$

and $$n =$$ no. of integers for which $$y$$ has min. value

Then $$\displaystyle\frac{m+n-18}{10} =$$
Maybe it's me, but I find that incomprehensible.

For a start why is $$m$$ not $$5152$$?

Do you mean $$n$$ to be the number of integers corresponding to a local minima of $$y$$? You can show that there is a global minimum and it achived this at two adjacent integer points.

(the slope is -5152 for -ve $$x$$, and increases by 2 when we pass a integer argument moving to the right ...)

CB

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