Pertenacious Polynomial Problem
by BadAtCompetitionMath21420, May 17, 2025, 3:13 AM
Let the polynomial 
have real roots and real coefficients with 
. What is the maximum value of 
?
This is a problem I made for my math competition, and I wanted to see if someone would double-check my work (No Mike allowed):
Is this solution good?
have real roots and real coefficients with 
. What is the maximum value of 
?This is a problem I made for my math competition, and I wanted to see if someone would double-check my work (No Mike allowed):
,
.
have roots 
.
.
(I won't be proving this here). This new information allows us to utilize the mean inequality chain as follows:
Similarly, applying AM-HM yields 
.
.Is this solution good?
This post has been edited 3 times. Last edited by BadAtCompetitionMath21420, 6 hours ago
Reason: No scrumptious allowed
Reason: No scrumptious allowed
,
and 
then find the value of 
and 
Show that
Let 
Show that
be the number of positive integers 
such that 
and 
divides
where 
denotes the number of positive integers that divide 
and 
.
From here we must have,
Observe that thus far the RHS of the divisibility statement has been strictly positive, following from the fact that 
for 
.
to be,
,
.
.
be 
,
.
?
,
such that 
is also prime.
vertices of an octagon each red, black, and white, such that no two adjacent sides are the same color?
and 
are points on the segments 
and 
,
and 
.
is 
,
?
consists of the union of disjoint pieces. Compute the distance between the endpoints of any one piece
April 2021
September 2020