How to solve inequality equation with ceil operator product I am trying to solve this inequality fo

Davon Irwin

Davon Irwin

Answered question

2022-06-07

How to solve inequality equation with ceil operator product
I am trying to solve this inequality for x:
c 1 x c 2 x N
With: c 1 , c 2 , x , N N and c 1 , c 2 , N being just constants.

Answer & Explanation

Samantha Reid

Samantha Reid

Beginner2022-06-08Added 22 answers

Step 1
Hint: first, let's consider the equation: c x = k , ,
where c , k , x N . This is equivalent to the following inequality
k 1 < c x k . .
If k = 1 then x c . For k > 1 we obtain
c k x < c k 1
and since we're interested only in natural solutions, we have
x [ c k , c k 1 ) N = { c k , c k + 1 , , c k 1 1 } ..
Now, to solve your problem you need to sum up the solutions of
{ c 1 x = k 1 c 2 x = k 2
for all pairs k 1 , k 2 N such that k 1 k 2 N .

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