Corresponding whole number values on a curve

[TuskB]

I’m new to calculus and have a conceptual question. For a given curve, would calculus be a tool that could predict if any whole numbers on the x axis will correspond with whole numbers on the Y axis?

I.e. curves with points that have corresponding whole number values on the X and Y planes. They don’t have to be equal values but must be whole with no fractions.

Thanks

 

[tkhunny]

"predict" - Not really a calculus concept.

"whole numbers" - Seek integer programming and various other things.

It is certainly possible that what you seek is out there. It is not an uncommon problem.

 

[Steven G]

I’m new to calculus and have a conceptual question. For a given curve, would calculus be a tool that could predict if any whole numbers on the x axis will correspond with whole numbers on the Y axis?

I.e. curves with points that have corresponding whole number values on the X and Y planes. They don’t have to be equal values but must be whole with no fractions.

Thanks

Hi, so what are your thoughts about this. Obviously you are going to evaluate the function at a whole number. Now you want to know which whole numbers yield back a whole number. Nice question. Calculus 1 or differential calculus is the study of rate of change. Personally I do not see how this could help solve your problem.

Let's look at this more concretely. Let x be a whole number and f(x) some function. You want |y-x| = whole number, |f(x)-x| = whole number. I'm trying my best to think how this can be done but can't see how to do it (mathematically). I am sure that given a function, Denis (a tutor on this site) would run a program to find some solutions (some (possibly all) if the domain is not finite, all if the domain is finite) but I do not see how else to do this.

 

[Dr.Peterson]

I’m new to calculus and have a conceptual question. For a given curve, would calculus be a tool that could predict if any whole numbers on the x axis will correspond with whole numbers on the Y axis?

I.e. curves with points that have corresponding whole number values on the X and Y planes. They don’t have to be equal values but must be whole with no fractions.

Thanks

Calculus really doesn't deal with whole numbers at all; in fact, it could be said to be the opposite, focusing on infinitesimal changes.

The field you want is number theory. Integer points on a curve are one of the topics studied there.

 

[TuskB]

Thanks you all for the feedback, It helps me with the orientation I was looking for, much appreciated.

 

[mmm4444bot]

… points that have corresponding whole number values on the X and Y planes …

Some notes about terminology. :cool:

X and Y are not planes; they're axes. You're talking about "coordinates", instead. (Together, the X-axis and Y-axis form an XY-plane.)

Also, the smallest Whole number is zero. If you want to include the numbers having no fractional part that are smaller than zero (i.e., negative cases), then refer to the set of Integers and write:

… (X,Y) points that have Integer coordinates …