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International Contests
Pan African
2003 Pan African
3
3
Part of
2003 Pan African
Problems
(2)
10101, 101010101
Source: Pan African 2003
10/4/2005
Does there exists a base in which the numbers of the form:
10101
,
101010101
,
1010101010101
,
⋯
10101, 101010101, 1010101010101,\cdots
10101
,
101010101
,
1010101010101
,
⋯
are all prime numbers?
number theory
prime numbers
Another functional equation
Source: Pan African 2003
10/4/2005
Find all functions
f
:
R
→
R
f: R\to R
f
:
R
→
R
such that:
f
(
x
2
)
−
f
(
y
2
)
=
(
x
+
y
)
(
f
(
x
)
−
f
(
y
)
)
,
x
,
y
∈
R
f(x^2)-f(y^2)=(x+y)(f(x)-f(y)), x,y \in R
f
(
x
2
)
−
f
(
y
2
)
=
(
x
+
y
)
(
f
(
x
)
−
f
(
y
))
,
x
,
y
∈
R
function