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National and Regional Contests
Germany Contests
German National Olympiad
1999 German National Olympiad
1
1
Part of
1999 German National Olympiad
Problems
(1)
x^2 +xy+y^2 = 97 diophantine
Source: Germany 1999 p1
2/23/2020
Find all
x
,
y
x,y
x
,
y
which satisfy the equality
x
2
+
x
y
+
y
2
=
97
x^2 +xy+y^2 = 97
x
2
+
x
y
+
y
2
=
97
, when
x
,
y
x,y
x
,
y
are a) natural numbers, b) integers
Diophantine equation
diophantine
number theory