OFFSET
1,3
COMMENTS
A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
A nontrivial cevian is one that does not coincide with a side of the triangle.
For an equilateral triangle of side n, the lengths of its cevians are the values of y in the solutions to x^2-y^2-n*x+n^2=0.
LINKS
Colin Barker, Table of n, a(n) for n = 1..10000
Wikipedia, Cevian
PROG
(PARI)
\\ Returns the length of the shortest integral cevian of an equilateral triangle of side n.
shortest(n) = {
s=[];
m=12*n^2;
fordiv(m, f,
g=m\f;
if(f<=g && (f+g)%2==0,
x=(f+g)\2;
if(x%4==0,
s=concat(s, x\4)
)
)
);
s=Colrev(s)~;
if(#s==1, return(0));
for(i=1, #s, if(s[i]!=n, return(s[i])))
}
vector(100, n, shortest(n))
CROSSREFS
KEYWORD
nonn
AUTHOR
Colin Barker, Sep 07 2014
STATUS
approved