Floor function

[lime]

How many solutions has the equation below in the interval [1, 100] ?

x^2 - [x^2] = {x}^2

here [x] - floor function, {x} - fractional part.

[Luma]

Let me give it a shot:
I don't know how to put this mathmatically, I think every number has a fraction part equals to (0.5) as the difference between the square and the floor of the sqaure will be (0.25) which is (0.5)²

[lime]

every number has a fraction part equals to (0.5)

This is not true. For example, f(x) = {x} in interval [0;1) {x} = x.

[Luma]

but the interval of [0:1) is not part of the solution interval [1:100], right?

[lime]

Ok. [1, 2) is a part of solution. On this interval {x} = x-1.

[Luma]

Here's another shot:
the numbers that has 0 in the units place and whatever in the fraction part ... because when those numbers are squared the fraction part is a complete square.

[lime]

Frankly, I didn't understand what you just said. Anyway, do you have an answer?

[Luma]

Originally Posted by lime

Frankly, I didn't understand what you just said. Anyway, do you have an answer?

I meant numbers like (10.x, 20.x, etc.)

[lime]

Apparently you're wrong. I don't know where though.

Btw. the question was asking "How many solutions ...", not "What are the numbers like ...".

Maybe you didn't understand the question?

[Luma]

Originally Posted by lime

Apparently you're wrong. I don't know where though.

Btw. the question was asking "How many solutions ...", not "What are the numbers like ...".

Maybe you didn't understand the question?

I was trying to find points where the equations has a solution then try to draw a conclusion but apparently this approach is inaccurate. I'll give it more thought before I post what I think