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Bosnia Herzegovina Team Selection Test
2002 Bosnia Herzegovina Team Selection Test
3
3
Part of
2002 Bosnia Herzegovina Team Selection Test
Problems
(1)
Solve for x,y,z in integers given p,q are distinct primes
Source: P5: Bosnia and Herzegovina TST 2002
10/7/2014
Let
p
p
p
and
q
q
q
be different prime numbers. Solve the following system in integers:
z
+
p
x
+
z
−
p
y
=
q
,
z
+
p
y
−
z
−
p
x
=
q
.
\frac{z+ p}x+\frac{z-p}y= q,\\ \frac{z+ p}y -\frac{z-p}x= q.
x
z
+
p
+
y
z
−
p
=
q
,
y
z
+
p
−
x
z
−
p
=
q
.
number theory
prime numbers
algebra proposed
algebra