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National and Regional Contests
New Zealand Contests
NZMOC Camp Selection Problems
2015 NZMOC Camp Selection Problems
4
4
Part of
2015 NZMOC Camp Selection Problems
Problems
(1)
diophantine (ab)^{2015} = (a^2 + b^2)^m
Source: New Zealand NZMOC Camp Selection Problems 2015 p4
9/19/2021
For which positive integers
m
m
m
does the equation:
(
a
b
)
2015
=
(
a
2
+
b
2
)
m
(ab)^{2015} = (a^2 + b^2)^m
(
ab
)
2015
=
(
a
2
+
b
2
)
m
have positive integer solutions?
number theory
Diophantine equation
diophantine