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Lusophon Mathematical Olympiad
2016 Lusophon Mathematical Olympiad
6
6
Part of
2016 Lusophon Mathematical Olympiad
Problems
(1)
Power of 2
Source:
7/29/2018
Source: Lusophon MO 2016 Prove that any positive power of
2
2
2
can be written as:
5
x
y
−
x
2
−
2
y
2
5xy-x^2-2y^2
5
x
y
−
x
2
−
2
y
2
where
x
x
x
and
y
y
y
are odd numbers.
Diophantine equation
power of 2
number theory