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The Philippines Contests
Philippine MO
2018 Philippine MO
4
An exponential diophantine equation
An exponential diophantine equation
Source: Philippines MO 2018/4
August 4, 2018
number theory
Diophantine equation
Problem Statement
Determine all ordered pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
of nonnegative integers that satisfy the equation
3
x
2
+
2
⋅
9
y
=
x
(
4
y
+
1
−
1
)
.
3x^2 + 2 \cdot 9^y = x(4^{y+1}-1).
3
x
2
+
2
⋅
9
y
=
x
(
4
y
+
1
−
1
)
.
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