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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
92
92
Part of
PEN A Problems
Problems
(1)
A 92
Source:
5/25/2007
Let
a
a
a
and
b
b
b
be positive integers. When
a
2
+
b
2
a^{2}+b^{2}
a
2
+
b
2
is divided by
a
+
b
,
a+b,
a
+
b
,
the quotient is
q
q
q
and the remainder is
r
.
r.
r
.
Find all pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
such that
q
2
+
r
=
1977
q^{2}+r=1977
q
2
+
r
=
1977
.
Divisibility Theory