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2018 IMAR Test
4
4
Part of
2018 IMAR Test
Problems
(1)
IMAR Test 2018 P4
Source: IMAR Test 2018 P4
4/21/2021
Prove that every non-negative integer
n
n
n
is expressible in the form
n
=
t
2
+
u
2
+
v
2
+
w
2
n=t^2+u^2+v^2+w^2
n
=
t
2
+
u
2
+
v
2
+
w
2
, where
t
,
u
,
v
,
w
t,u,v,w
t
,
u
,
v
,
w
are integers such that
t
+
u
+
v
+
w
t+u+v+w
t
+
u
+
v
+
w
is a perfect square.* * *
number theory
romania
Perfect Squares