MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
1998 India National Olympiad
3
3
Part of
1998 India National Olympiad
Problems
(1)
Divisiblity by 5
Source: INMO 1998 Problem 3
10/7/2005
Let
p
,
q
,
r
,
s
p , q, r , s
p
,
q
,
r
,
s
be four integers such that
s
s
s
is not divisible by
5
5
5
. If there is an integer
a
a
a
such that
p
a
3
+
q
a
2
+
r
a
+
s
pa^3 + qa^2+ ra +s
p
a
3
+
q
a
2
+
r
a
+
s
is divisible be 5, prove that there is an integer
b
b
b
such that
s
b
3
+
r
b
2
+
q
b
+
p
sb^3 + rb^2 + qb + p
s
b
3
+
r
b
2
+
q
b
+
p
is also divisible by 5.
number theory solved
number theory