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Problems
Contests
National and Regional Contests
PEN Problems
PEN D Problems
17
17
Part of
PEN D Problems
Problems
(1)
D 17
Source:
5/25/2007
Determine all positive integers
n
n
n
such that
x
y
+
1
≡
0
(
m
o
d
n
)
xy+1 \equiv 0 \; \pmod{n}
x
y
+
1
≡
0
(
mod
n
)
implies that
x
+
y
≡
0
(
m
o
d
n
)
x+y \equiv 0 \; \pmod{n}
x
+
y
≡
0
(
mod
n
)
.
modular arithmetic
Congruences