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Swedish Mathematical Competition
1997 Swedish Mathematical Competition
3
3
Part of
1997 Swedish Mathematical Competition
Problems
(1)
every integer can be written in the form x^2 -y^2 +Ax+By where A+B= odd
Source: 1997 Swedish Mathematical Competition p3
4/2/2021
Let
A
A
A
and
B
B
B
be integers with an odd sum. Show that every integer can be written in the form
x
2
ā
y
2
+
A
x
+
B
y
x^2 -y^2 +Ax+By
x
2
ā
y
2
+
A
x
+
B
y
, where
x
,
y
x,y
x
,
y
are integers.
number theory
odd