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2023 China Northern MO
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2023 China Northern MO
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(1)
China Northern Mathematical Olympiad 2023 , Problem 3
Source: China 10 Aug
8/11/2023
Find all solutions of the equation
s
i
n
π
x
+
c
o
s
π
x
=
(
−
1
)
⌊
x
⌋
sin\pi \sqrt x+cos\pi \sqrt x=(-1)^{\lfloor \sqrt x \rfloor }
s
inπ
x
+
cos
π
x
=
(
−
1
)
⌊
x
⌋
equations
floor function
algebra