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Tuymaada Olympiad
2017 Tuymaada Olympiad
1
1
Part of
2017 Tuymaada Olympiad
Problems
(1)
Tuymaada 2017 P1 Day1 Senior League
Source:
7/25/2017
Functions
f
f
f
and
g
g
g
are defined on the set of all integers in the interval
[
−
100
;
100
]
[-100; 100]
[
−
100
;
100
]
and take integral values. Prove that for some integral
k
k
k
the number of solutions of the equation
f
(
x
)
−
g
(
y
)
=
k
f(x)-g(y)=k
f
(
x
)
−
g
(
y
)
=
k
is odd.\\ ( A. Golovanov)
function
algebra