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Problems
Contests
National and Regional Contests
PEN Problems
PEN P Problems
36
36
Part of
PEN P Problems
Problems
(1)
P 36
Source:
5/25/2007
Let
k
k
k
and
s
s
s
be odd positive integers such that
3
k
−
2
−
1
≤
s
≤
4
k
.
\sqrt{3k-2}-1 \le s \le \sqrt{4k}.
3
k
−
2
−
1
≤
s
≤
4
k
.
Show that there are nonnegative integers
t
t
t
,
u
u
u
,
v
v
v
, and
w
w
w
such that
k
=
t
2
+
u
2
+
v
2
+
w
2
,
and
s
=
t
+
u
+
v
+
w
.
k=t^{2}+u^{2}+v^{2}+w^{2}, \;\; \text{and}\;\; s=t+u+v+w.
k
=
t
2
+
u
2
+
v
2
+
w
2
,
and
s
=
t
+
u
+
v
+
w
.
Additive Number Theory