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Singapore Senior Math Olympiad
2004 Singapore MO Open
2
2
Part of
2004 Singapore MO Open
Problems
(1)
x^2 + ax + b = 167 y, 1<=a,b<=2004 , no of ordered solutions (a,b)
Source: Singapore Open Math Olympiad 2004 2nd Round p2 SMO
4/3/2020
Find the number of ordered pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of integers, where
1
≤
a
,
b
≤
2004
1 \le a, b \le 2004
1
≤
a
,
b
≤
2004
, such that
x
2
+
a
x
+
b
=
167
y
x^2 + ax + b = 167 y
x
2
+
a
x
+
b
=
167
y
has integer solutions in
x
x
x
and
y
y
y
. Justify your answer.
number theory
diophantine
Diophantine equation