[/quote]
,
,
.
that satisfies:
such that 
is a perfect square.
such that, for every positive integer 
the integer
is a multiple of 
(Note that 
denotes the greatest integer less than or equal to 
For example, 
and 
)
If the value of 
can be written as 
where m and n are co-prime positive integers then find the value of 
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 
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 
.
,
,
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 
Y by cubres
Given a circle with chord AB. k and l are tangents to the circle at points A and B. C and E are in different half-planes with respect to AB and lie on k, and F and D are in different half-planes with respect to AB and lie on l. Furthermore, C and F are in the same half-plane with respect to AB and AC = BD; AE = BF. CD intersects the circle at P and R and EF intersects the circle at Q and S. P and Q are in the same half-plane with respect to AB and in different half-plane with R and S. Prove that PQRS is a parallelogram if and only if AB, CD, and EF intersect at one point.
This post has been edited 3 times. Last edited by iv999xyz, Apr 12, 2025, 10:26 AM
Reason: error
Reason: error
.
are tangents to the circle at points 
and 
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= 
.
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.
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