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National and Regional Contests
Turkey Contests
Akdeniz University MO
1999 Akdeniz University MO
2
2
Part of
1999 Akdeniz University MO
Problems
(2)
number theory
Source:
1/31/2016
Prove that, we can't find positive numbers
m
m
m
and
n
n
n
such that,
m
2
+
(
m
+
1
)
2
=
n
4
+
(
n
+
1
)
4
m^2+(m+1)^2=n^4+(n+1)^4
m
2
+
(
m
+
1
)
2
=
n
4
+
(
n
+
1
)
4
number theory
number theory
Source:
1/31/2016
Find all
(
x
,
y
)
(x,y)
(
x
,
y
)
real numbers pairs such that,
x
7
+
y
7
=
x
4
+
y
4
x^7+y^7=x^4+y^4
x
7
+
y
7
=
x
4
+
y
4
number theory