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Polish MO Finals
1971 Polish MO Finals
4
min (x,y)>= n if x^n + y^n = z^n
min (x,y)>= n if x^n + y^n = z^n
Source: Polish MO Finals 1971 p4
August 22, 2024
number theory
diophantine
Problem Statement
Prove that if positive integers
x
,
y
,
z
x,y,z
x
,
y
,
z
satisfy the equation
x
n
+
y
n
=
z
n
,
x^n + y^n = z^n,
x
n
+
y
n
=
z
n
,
then
min
(
x
,
y
)
≥
n
\min\, (x,y) \ge n
min
(
x
,
y
)
≥
n
.
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