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2
j^2 +k^2 +l^2 +m^2 +n^2 = jklmn-12 , exist integers >100
j^2 +k^2 +l^2 +m^2 +n^2 = jklmn-12 , exist integers >100
Source: Ukrainian TST 1999 p2
February 13, 2020
Integers
algebra
Problem Statement
Show that there exist integers
j
,
k
,
l
,
m
,
n
j,k,l,m,n
j
,
k
,
l
,
m
,
n
greater than
100
100
100
such that
j
2
+
k
2
+
l
2
+
m
2
+
n
2
=
j
k
l
m
n
ā
12
j^2 +k^2 +l^2 +m^2 +n^2 = jklmn-12
j
2
+
k
2
+
l
2
+
m
2
+
n
2
=
jk
l
mn
ā
12
.
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