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Romania Team Selection Test
2022 Romania Team Selection Test
4
4
Part of
2022 Romania Team Selection Test
Problems
(1)
Romania TST 2022 Day 2 P4
Source: Romania TST 2022
5/15/2022
Any positive integer
N
N
N
which can be expressed as the sum of three squares can obviously be written as
N
=
a
2
+
b
2
+
c
2
+
d
2
1
+
a
b
c
d
N=\frac{a^2+b^2+c^2+d^2}{1+abcd}
N
=
1
+
ab
c
d
a
2
+
b
2
+
c
2
+
d
2
where
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are nonnegative integers. Is the mutual assertion true?
number theory
Perfect Squares
romania
Romanian TST