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2014 Indonesia MO Shortlist
A2
A2
Part of
2014 Indonesia MO Shortlist
Problems
(1)
Equal sum elements for equal product indices
Source: Indonesian Mathematical Olympiad 2014 Day 2 Problem 5
9/4/2014
A sequence of positive integers
a
1
,
a
2
,
…
a_1, a_2, \ldots
a
1
,
a
2
,
…
satisfies
a
k
+
a
l
=
a
m
+
a
n
a_k + a_l = a_m + a_n
a
k
+
a
l
=
a
m
+
a
n
for all positive integers
k
,
l
,
m
,
n
k,l,m,n
k
,
l
,
m
,
n
satisfying
k
l
=
m
n
kl = mn
k
l
=
mn
. Prove that if
p
p
p
divides
q
q
q
then
a
p
≤
a
q
a_p \le a_q
a
p
≤
a
q
.
number theory unsolved
number theory