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1
xy - x - y + 1., ab = 0 if |a + b| > |1 + ab| - 2010 Romania District VII p1
xy - x - y + 1., ab = 0 if |a + b| > |1 + ab| - 2010 Romania District VII p1
Source:
September 1, 2024
number theory
algebra
Problem Statement
a) Factorize
x
y
−
x
−
y
+
1
xy - x - y + 1
x
y
−
x
−
y
+
1
.b) Prove that if integers
a
a
a
and
b
b
b
satisfy
∣
a
+
b
∣
>
∣
1
+
a
b
∣
|a + b| > |1 + ab|
∣
a
+
b
∣
>
∣1
+
ab
∣
, then
a
b
=
0
ab = 0
ab
=
0
.
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