[/quote]
,
positive integers 
such that for every index 
,
,
is a multiple of 
.
and 
be positive integers satisfying the equation ![$(a, b) + [a, b]=2021^c$](http://latex.artofproblemsolving.com/2/4/6/246ccbb22acecb7adc72219afb8afb34c9b05101.png)
.
is a prime number, prove that the number 
is composite.
be the set of real numbers. Determine all functions 
such that ![\[ f(x^2 - y^2) = x f(x) - y f(y) \]](http://latex.artofproblemsolving.com/6/8/f/68f78e0df627f6ac04052433c01627bf16f0af8e.png)
for all pairs of real numbers 
and 
.
feet and area 
into 
or 
can sometimes be quite complex. That's why I’ve written a program to assist with this process.
be real numbers such that 
Prove that 
Where 
with odd integer side lengths is divided into small rectangles with integer side lengths. Prove that there is at least one among the small rectangles whose distances from the four sides of 
Prove that 
,
,
,
can be expressed by a sum of positive integers 
'![\[n=a_1+a_2+\dots+a_m,\]](http://latex.artofproblemsolving.com/6/c/2/6c2a979a5ff6c40bf2d7152c8c32088fc36f848b.png)
where 
,
,
,
and 
.
equally spaced points on a circular track 
of circumference 
in some order, each label used once. Initially, Bunbun the Bunny begins at 
.
,
,
,
to 
,
of 
is a diameter of 
Y by
I am practicing previous years' MathCount papers, but they seem to get progressively harder each year.
So, for those of you who scored well in Mathcounts, how many sprint questions are/were you able to do in State/Nationals?
I want to get a sense of where I stand.
Thanks in advance!
So, for those of you who scored well in Mathcounts, how many sprint questions are/were you able to do in State/Nationals?
I want to get a sense of where I stand.
Thanks in advance!
This post has been edited 1 time. Last edited by kp34912, Mar 27, 2025, 9:27 AM
Reason: edited
Reason: edited
i mock ~30 total on nats from after 2020 
