MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
37
37
Part of
PEN H Problems
Problems
(1)
H 37
Source:
5/25/2007
Prove that for each positive integer
n
n
n
there exist odd positive integers
x
n
x_n
x
n
and
y
n
y_n
y
n
such that
x
n
2
+
7
y
n
2
=
2
n
{x_{n}}^2 +7{y_{n}}^2 =2^n
x
n
2
+
7
y
n
2
=
2
n
.
modular arithmetic
Diophantine Equations