How can I implement infinite scrolling by scrolling Skybox's texture, not the entity?

How can I implement infinite scrolling by scrolling Skybox's texture, not the entity?

I'm writing a 2D platformer game on Java with LWJGL. I'm doing this just for the sake of learning and not the result itself, so when I decided to implement scrolling I did it two ways I could invent myself:
Three "sky" rectangle entities that located in a row and when my camera is moved to the right (fully on third), I move my first rectangle (from the far left) to the far right, etc. Pretty sure it can be made that way only with two entities, but I didn't have enough motivation to do it right now.
Not infinite, but you can just stack these Sky entities in a row for the whole level width. Very lame approach.
But I realised that to optimize it, I can move not the "canvas", but the "painting" on the "canvas" itself. So, is it possible to move it this way? I'm not entirely sure that's possible at all, but I think it should be. How I see it: I change not position.x or position.y, but the texture coordinates, they should repeat, aren't they?



My code, if that will be helpful anyway. Render function in Main class:
private void render() {
    setupGL();
    GL11.glPushMatrix();
        GL11.glTranslatef(-Camera.x, -Camera.y, 0.0f);
        GL11.glScissor(0, 0, SCREEN_WIDTH, SCREEN_HEIGHT);
        sky.draw();
    GL11.glPopMatrix();
}
Draw function of the Sky entity, and yes, I know that immediate mode is bad, but I still haven't got my hands on arrays and other drawing methods.
public void draw() {
    GL11.glBindTexture(GL11.GL_TEXTURE_2D, TextureWrapper.get(EntityTypes.SKY).getTextureID());
    GL11.glColor3f(1.0f, 1.0f, 1.0f);
    GL11.glBegin(GL11.GL_QUADS);
        GL11.glTexCoord2f(0.0f, 1);
        GL11.glVertex2f(this.x, this.y + this.height);

        GL11.glTexCoord2f(1, 1);
        GL11.glVertex2f(this.x + this.width, this.y + this.height);

        GL11.glTexCoord2f(1, 0);
        GL11.glVertex2f(this.x + this.width, this.y);

        GL11.glTexCoord2f(0.0f, 0);
        GL11.glVertex2f(this.x, this.y);
    GL11.glEnd();
    GL11.glBindTexture(GL11.GL_TEXTURE_2D, 0);
}