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Romanian Masters of Mathematics Collection
2016 Romanian Master of Mathematics Shortlist
A1
A1
Part of
2016 Romanian Master of Mathematics Shortlist
Problems
(1)
f(a + b) = f(a) + f(b) + f(c) + f(d) in N-{O}, with 2ab = c^2 + d^2
Source: RMM Shortlist 2016 A1
7/4/2019
Determine all functions
f
f
f
from the set of non-negative 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
)
, whenever
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
, are non-negative integers satisfying
2
a
b
=
c
2
+
d
2
2ab = c^2 + d^2
2
ab
=
c
2
+
d
2
.
functional equation
algebra
functional equation in N