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Putnam
2005 Putnam
B1
B1
Part of
2005 Putnam
Problems
(1)
Putnam 2005 B1
Source:
12/5/2005
Find a nonzero polynomial
P
(
x
,
y
)
P(x,y)
P
(
x
,
y
)
such that
P
(
⌊
a
⌋
,
⌊
2
a
⌋
)
=
0
P(\lfloor a\rfloor,\lfloor 2a\rfloor)=0
P
(⌊
a
⌋
,
⌊
2
a
⌋)
=
0
for all real numbers
a
.
a.
a
.
(Note:
⌊
v
⌋
\lfloor v\rfloor
⌊
v
⌋
is the greatest integer less than or equal to
v
.
v.
v
.
)
Putnam
algebra
polynomial
floor function
inequalities
function
college contests