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44
2000 Guts #44: Function over integers
2000 Guts #44: Function over integers
Source:
October 25, 2014
function
Problem Statement
A function
f
:
Z
⟹
Z
f:\mathbb{Z}\implies\mathbb{Z}
f
:
Z
⟹
Z
satisfies
f
(
x
+
4
)
−
f
(
x
)
=
8
x
+
20
f(x+4)-f(x)=8x+20
f
(
x
+
4
)
−
f
(
x
)
=
8
x
+
20
f
(
x
2
−
1
)
=
(
f
(
x
)
−
x
)
2
+
x
2
−
2
f(x^2-1)=(f(x)-x)^2+x^2-2
f
(
x
2
−
1
)
=
(
f
(
x
)
−
x
)
2
+
x
2
−
2
Find
f
(
0
)
f(0)
f
(
0
)
and
f
(
1
)
f(1)
f
(
1
)
.
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