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1984 All Soviet Union Mathematical Olympiad
379
ASU 379 All Soviet Union MO 1984 diophant (5+3\sqrt2)^m=(3+5\sqrt2)^n
ASU 379 All Soviet Union MO 1984 diophant (5+3\sqrt2)^m=(3+5\sqrt2)^n
Source:
August 5, 2019
diophantine
Diophantine equation
number theory
algebra
exponential
Problem Statement
Find integers
m
m
m
and
n
n
n
such that
(
5
+
3
2
)
m
=
(
3
+
5
2
)
n
(5 + 3 \sqrt2)^m = (3 + 5 \sqrt2)^n
(
5
+
3
2
)
m
=
(
3
+
5
2
)
n
.
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