Register to reply

Number of lattice points between y=ax+b and y=x^2?

by SeventhSigma
Tags: lattice, number, points
Share this thread:
SeventhSigma
#1
Nov25-12, 11:12 AM
P: 250
Is there a nice closed-form for this?
Phys.Org News Partner Science news on Phys.org
'Office life' of bacteria may be their weak spot
Lunar explorers will walk at higher speeds than thought
Philips introduces BlueTouch, PulseRelief control for pain relief
ramsey2879
#2
Nov25-12, 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?
SeventhSigma
#3
Nov25-12, 06:51 PM
P: 250
The integral lattice points in the area formed between the two curves

ramsey2879
#4
Nov26-12, 06:05 PM
P: 894
Number of lattice points between y=ax+b and y=x^2?

Quote Quote by SeventhSigma View Post
Is there a nice closed-form for this?
Solve the Quadratic equation x^2 - ax - b = 0 to get x small and x large. Then from the ceiling of x small to the floor of x large, sum ax+b +1 - x^2 for integer values of x. I think that will give you your sum.

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 x-small and x-large. 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