MathDB
Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Ukraine Team Selection Test
2016 Ukraine Team Selection Test
2
2
Part of
2016 Ukraine Team Selection Test
Problems
(1)
Function
Source: Already posted
5/13/2018
Find all functions from positive integers to itself such that
f
(
a
+
b
)
=
f
(
a
)
+
f
(
b
)
+
f
(
c
)
+
f
(
d
)
f(a+b)=f(a)+f(b)+f(c)+f(d)
f
(
a
+
b
)
=
f
(
a
)
+
f
(
b
)
+
f
(
c
)
+
f
(
d
)
for all
c
2
+
d
2
=
2
a
b
c^2+d^2=2ab
c
2
+
d
2
=
2
ab
function