[/quote]
,
If we set 
then it's the unique polynomial such that for all integers 
In general, for each positive integer k,there is a unique polynomial 
such that 
Find the value of 
for 
and 
if 
then find the coefficient of 
in 
be a fixed acute triangle inscribed in a circle 
with center 
.
is chosen on minor arc 
of 
and 
.
and 
the circumcenters of triangles 
and 
,
is minimized.
such that:
be a prime and 
a nonempty set. Suppose that for each element 
there exist elements 
,
such that 
is divisible by 
,
denotes the cardinality of 
.
different point-like cities were founded one by one; from the second onwards, each newly founded city and the nearest existing city (the older one, if there were two) were declared sister cities. The surviving map of the empire shows the cities and the distances between them, but not the order in which they were founded. Historians have tried to deduce from the map that each city had at most 41 sister cities.
,
,
is divided into cyclic quadrilaterals with pairwise disjoint interiors. None of the vertices of the cyclic quadrilaterals in the decomposition is an interior point of a side of any cyclic quadrilateral in the decomposition or of a side of the quadrilateral 
and a positive integer 
.
is an integer. Is it true that for each perfect polynomial 
so that for each integer 
for which 
with the property that 
is divisible by 
.
Y by john0512
9Poll:
Do you prefer RSM (Russian School of Math) or AoPS?
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I'm doing RSM right now, but I want to switch over to AoPS. I'm just curious to know, which do you prefer? (If you have no experience with both, please don't vote!)
If you want, please drop some advice on the Intermediate Algebra class, because that's the one I'm hoping to take!
If you want, please drop some advice on the Intermediate Algebra class, because that's the one I'm hoping to take!
This post has been edited 1 time. Last edited by BlazingSun1200, Mar 21, 2021, 3:08 AM
