Let F(x) be a polynomial with integer coefficients.
There are two distinct points on the graph of F, say P and Q, with integer coordinates.
If the length of PQ is an integer, then will PQ always be parallel to the x-axis?
If so, prove it.
If not, provide an example.
Let F(x) a polynomial
with integer coefficients such that {0,0} and {x1,y1} are distinct points P, Q on the graph of F.
x1 and y1 need only be elements of a PPT, i.e. (x1^2+y1^2)=z^2 for some integer z. For example, if x1=3 and y1=4, then then P and Q are exactly 5 apart.
Line pq is not then parallel to the x-axis.
Example: 4x-3y=0
Edited on July 10, 2023, 7:52 am
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Posted by broll
on 2023-07-10 06:15:43 |
Seems unlikely
