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District Olympiad
2001 District Olympiad
1
Romania District Olympiad 2001 - VIII Grade
Romania District Olympiad 2001 - VIII Grade
Source:
March 12, 2011
number theory proposed
number theory
Problem Statement
a) Find all the integers
m
m
m
and
n
n
n
such that
9
m
2
+
3
n
=
n
2
+
8
9m^2+3n=n^2+8
9
m
2
+
3
n
=
n
2
+
8
b) Let
a
,
b
∈
N
∗
a,b\in \mathbb{N}^*
a
,
b
∈
N
∗
. If
x
=
a
a
+
b
+
(
a
+
b
)
a
x=a^{a+b}+(a+b)^a
x
=
a
a
+
b
+
(
a
+
b
)
a
and
y
=
a
a
+
(
a
+
b
)
a
+
b
y=a^a+(a+b)^{a+b}
y
=
a
a
+
(
a
+
b
)
a
+
b
which one is bigger?Florin Nicoara, Valer Pop
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