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.
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Mr. Fat and Mr. Taf play a game with a polynomial of degree at least 4: 
They fill in real numbers to empty spaces (the coefficients of the terms other than 
and the constant term) in turn. If the resulting polynomial has no real root, Mr. Fat wins; otherwise, Mr. Taf wins. If Mr. Fat goes first, who has a winning strategy?
They fill in real numbers to empty spaces (the coefficients of the terms other than 
and the constant term) in turn. If the resulting polynomial has no real root, Mr. Fat wins; otherwise, Mr. Taf wins. If Mr. Fat goes first, who has a winning strategy?This post has been edited 1 time. Last edited by Yiyj1, Apr 9, 2025, 3:18 AM
