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Korea Junior Mathematics Olympiad
2017 Korea Junior Math Olympiad
5
m^3+am+b is not a multiple of n
m^3+am+b is not a multiple of n
Source: KJMO 2017 p5
July 26, 2019
number theory
KJMO
Problem Statement
Given an integer
n
≥
2
n\ge 2
n
≥
2
, show that there exist two integers
a
,
b
a,b
a
,
b
which satisfy the following.For all integer
m
m
m
,
m
3
+
a
m
+
b
m^3+am+b
m
3
+
am
+
b
is not a multiple of
n
n
n
.
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