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Baltic Way
2015 Baltic Way
19
19
Part of
2015 Baltic Way
Problems
(1)
Triangle Sides
Source: Baltic Way 2015
11/8/2015
Three pairwairs distinct positive integers
a
,
b
,
c
,
a,b,c,
a
,
b
,
c
,
with
g
c
d
(
a
,
b
,
c
)
=
1
gcd(a,b,c)=1
g
c
d
(
a
,
b
,
c
)
=
1
, satisfy
a
∣
(
b
−
c
)
2
,
b
∣
(
a
−
c
)
2
,
c
∣
(
a
−
b
)
2
a|(b-c)^2 ,b|(a-c)^2 , c|(a-b)^2
a
∣
(
b
−
c
)
2
,
b
∣
(
a
−
c
)
2
,
c
∣
(
a
−
b
)
2
Prove that there doesnt exist a non-degenerate triangle with side lengths
a
,
b
,
c
.
a,b,c.
a
,
b
,
c
.
Triangle
Sides of a triangle
number theory