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National and Regional Contests
South Africa Contests
South Africa National Olympiad
1997 South africa National Olympiad
3
3
Part of
1997 South africa National Olympiad
Problems
(1)
Diophantine equation with powers of 2 and 3
Source: South Africa 1997
10/8/2005
Find all solutions
x
,
y
∈
Z
x,y \in \mathbb{Z}
x
,
y
∈
Z
,
x
,
y
≥
0
x,y \geq 0
x
,
y
≥
0
, to the equation
1
+
3
x
=
2
y
.
1 + 3^x = 2^y.
1
+
3
x
=
2
y
.