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Baltic Way
1995 Baltic Way
3
3
Part of
1995 Baltic Way
Problems
(1)
b+c is square of an integer
Source: Baltic Way 1995
10/8/2011
The positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
are pairwise relatively prime,
a
a
a
and
c
c
c
are odd and the numbers satisfy the equation
a
2
+
b
2
=
c
2
a^2+b^2=c^2
a
2
+
b
2
=
c
2
. Prove that
b
+
c
b+c
b
+
c
is the square of an integer.
number theory
relatively prime
number theory proposed