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Nordic
2014 Nordic
1
1
Part of
2014 Nordic
Problems
(1)
f(x^2) - f(y^2) = f(x + y)f(x - y)
Source: Nordic Mathematical Contest 2014 #1
9/23/2017
Find all functions
f
:
N
→
N
{ f : N \rightarrow N}
f
:
N
→
N
(where
N
{N}
N
is the set of the natural numbers and is assumed to contain
0
{0}
0
), such that
f
(
x
2
)
−
f
(
y
2
)
=
f
(
x
+
y
)
f
(
x
−
y
)
{f(x^2) - f(y^2) = f(x + y)f(x - y)}
f
(
x
2
)
−
f
(
y
2
)
=
f
(
x
+
y
)
f
(
x
−
y
)
for all
x
,
y
∈
N
{x, y \in N}
x
,
y
∈
N
with
x
≥
y
{x \ge y}
x
≥
y
.
functional equation
function
algebra