Register to reply 
Number of lattice points between y=ax+b and y=x^2? 
Share this thread: 
#1
Nov2512, 11:12 AM

P: 250

Is there a nice closedform for this?



#2
Nov2512, 05:49 PM

P: 894

Since a straight line intercepts a parabola in at most two points, I believe your looking for the number of lattice points on both the curve and straight line that surround the area between the two lines. Is that right? Otherwise the answer would be one of either 0,1,2 or infinity. Infinity would be if you include all lattice points on the parabola, not just those bordering the area. Then again you may be looking for the number of coordinite points within the area so I am unsure what you are looking for. Also, should we assume that a and b are integers?



#3
Nov2512, 06:51 PM

P: 250

The integral lattice points in the area formed between the two curves



#4
Nov2612, 06:05 PM

P: 894

Number of lattice points between y=ax+b and y=x^2?
Final Edit: the above includes the lattice points of the lines, to exclude them, sum the value "ax + b 1  x^2" for integer values between xsmall and xlarge. Both sums assume that "a" and "b" are integers. 


Register to reply 
Related Discussions  
Number of points on the plane vs. number of points on the line  Set Theory, Logic, Probability, Statistics  13  
Lattice points  Precalculus Mathematics Homework  2  
Lattice Points  Linear & Abstract Algebra  7  
Lattice points  Calculus & Beyond Homework  1  
LAttice Points  Introductory Physics Homework  19 