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2
Function
Function
Source: Already posted
May 13, 2018
function
Problem Statement
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
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