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All-Russian Olympiad
1997 All-Russian Olympiad
3
m + n = gcd(m; n)^2 ...
m + n = gcd(m; n)^2 ...
Source: ARMO 1997, 10.7
April 20, 2013
number theory proposed
number theory
Problem Statement
Find all triples
m
m
m
;
n
n
n
;
l
l
l
of natural numbers such that
m
+
n
=
g
c
d
(
m
;
n
)
2
m + n = gcd(m; n)^2
m
+
n
=
g
c
d
(
m
;
n
)
2
;
m
+
l
=
g
c
d
(
m
;
l
)
2
m + l = gcd(m; l)^2
m
+
l
=
g
c
d
(
m
;
l
)
2
;
n
+
l
=
g
c
d
(
n
;
l
)
2
n + l = gcd(n; l)^2
n
+
l
=
g
c
d
(
n
;
l
)
2
: S. Tokarev
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