How To Solve An Equation That Has "Int" In The Mix

Reply #6

JADELottery — Fri, 05 Jul 2019 17:10:34 GMT

Decimal Integer Part Fractional Part

if = . , then int( ) = .0 and frac( ) = 0.

Relational Equations

= int( ) + frac( )

int( ) = - frac( )

frac( ) = - int( )

Solution

a = (b x + c) - int((b x + c) / n) n

a / n = ((b x + c) / n) - int((b x + c) / n)

a / n = frac((b x + c) / n)

if and only if |a| |n| and 0 (a / n) 1, then | | + (a / n) = (b x + c) / n

n | | + a = b x + c

n | | + a - c = b x

(n | | + a - c) / b = x

x = (n | | + a - c) / b

Reply #5

JADELottery — Fri, 05 Jul 2019 04:54:43 GMT

Thanks.

Hope your 4th was great, too.

Been lurking around mostly due to business travel and vacation.

Reply #4

lakerben — Fri, 05 Jul 2019 04:08:25 GMT

Happy 4th jade! Good to see you on the site

Reply #3

JADELottery — Fri, 05 Jul 2019 02:04:30 GMT

Solveable, yes.

If a n

Reply #2

mitachoo — Thu, 04 Jul 2019 23:46:32 GMT

Thanks cottoneyedjoe, in a roundabout way I figured there was an infinte number of solutions in that I had resorted to creating a Macro in Excel to iterate on solutions but only up to a certain value of a. I hoped there might be a better way, but if infinity is the answer, there's naught I can do except bound it as I've done already.

Thanks again

Reply #1

cottoneyedjoe — Thu, 04 Jul 2019 20:13:47 GMT

Assuming n is an integer and k is either an integer or non-integer, the expression int{ k/n }*n is an integer bounded between a minimum of int{k} - n + 1 and a maximum of int{k}. That is a total of n different values the expression can take on, so to do it algebraically, you could replace k with bx+c and solve n different equations.

What you will find is that for any given value of a that is at least 0 and strictly less than n, there are infinitely many values of x that make the equation true... [ More ]

How To Solve An Equation That Has "Int" In The Mix

mitachoo — Thu, 04 Jul 2019 17:53:59 GMT

I have an odd math question, hopefully someone can point me in the right direction.

I have an equation that looks like this:

a = (bx + c) - int{ (bx + c)/n } * n

How the (expletive) do I solve for x, since x has a mix of Int and non-Int? Is there some way to convert the Int portion of the equation to non-Int