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Moscow Mathematical Olympiad
1955 Moscow Mathematical Olympiad
307
307
Part of
1955 Moscow Mathematical Olympiad
Problems
(1)
MMO 307 Moscow MO 1955 ax^2+bx+c= square for any integer x
Source:
8/17/2019
* The quadratic expression
a
x
2
+
b
x
+
c
ax^2 + bx + c
a
x
2
+
b
x
+
c
is a square (of an integer) for any integer
x
x
x
. Prove that
a
x
2
+
b
x
+
c
=
(
d
x
+
e
)
2
ax^2 + bx + c = (dx + e)^2
a
x
2
+
b
x
+
c
=
(
d
x
+
e
)
2
for some integers d and e.
trinomial
Perfect Square
number theory
algebra