MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Polish MO Finals
1957 Polish MO Finals
3
3
Part of
1957 Polish MO Finals
Problems
(1)
ax^2 + bx + c takes an integer value for every integer x
Source: Polish MO Finals 1957 p3
8/29/2024
Prove that if the function
a
x
2
+
b
x
+
c
ax^2 + bx + c
a
x
2
+
b
x
+
c
takes an integer value for every integer value of the variable
x
x
x
, then
2
a
2a
2
a
,
a
+
b
a + b
a
+
b
,
c
c
c
are integers and vice versa.
number theory
Integer