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National and Regional Contests
Germany Contests
Bundeswettbewerb Mathematik
1971 Bundeswettbewerb Mathematik
1
Never a prime
Never a prime
Source:
April 13, 2005
Problem Statement
For any positive integers
a
,
b
,
c
,
d
,
n
a,b,c,d,n
a
,
b
,
c
,
d
,
n
, it is given that
n
n
n
is composite, such that
n
=
a
b
=
c
d
n=ab=cd
n
=
ab
=
c
d
and
S
S
S
as
S
=
a
2
+
b
2
+
c
2
+
d
2
S=a^2+b^2+c^2+d^2
S
=
a
2
+
b
2
+
c
2
+
d
2
Prove that
S
S
S
is never a prime number
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