MathDB
Problems
Contests
International Contests
Baltic Way
1999 Baltic Way
20
20
Part of
1999 Baltic Way
Problems
(1)
Determine all values of a^2+b^2+c^2+d^2 for primes a,b,c,d
Source: Baltic Way 1999
12/23/2010
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
and
d
d
d
be prime numbers such that
a
>
3
b
>
6
c
>
12
d
a>3b>6c>12d
a
>
3
b
>
6
c
>
12
d
and
a
2
−
b
2
+
c
2
−
d
2
=
1749
a^2-b^2+c^2-d^2=1749
a
2
−
b
2
+
c
2
−
d
2
=
1749
. Determine all possible values of
a
2
+
b
2
+
c
2
+
d
2
a^2+b^2+c^2+d^2
a
2
+
b
2
+
c
2
+
d
2
.
number theory
prime numbers
number theory proposed