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Singapore Junior Math Olympiad
2023 Singapore Junior Math Olympiad
5
5
Part of
2023 Singapore Junior Math Olympiad
Problems
(1)
Diophantine Equation
Source: 2023 Singapore MO Round 2 Senior Q2 / Junior Q5
6/24/2023
Find all positive integers
k
k
k
such that there exists positive integers
a
,
b
a, b
a
,
b
such that
a
2
+
4
=
(
k
2
ā
4
)
b
2
.
a^2+4=(k^2-4)b^2.
a
2
+
4
=
(
k
2
ā
4
)
b
2
.
number theory
Diophantine equation