MathDB
Problems
Contests
National and Regional Contests
Peru Contests
Peru Iberoamerican Team Selection Test
2008 Peru Iberoamerican Team Selection Test
2008 Peru Iberoamerican Team Selection Test
Part of
Peru Iberoamerican Team Selection Test
Subcontests
(1)
P1
1
Hide problems
Solve equation with least prime divisors
For every integer
m
>
1
m>1
m
>
1
, let
p
(
m
)
p(m)
p
(
m
)
be the least prime divisor of
m
m
m
. If
a
a
a
and
b
b
b
are integers greater than
1
1
1
such that:
a
2
+
b
=
p
(
a
)
+
[
p
(
b
)
]
2
a^2+b=p(a)+[p(b)]^2
a
2
+
b
=
p
(
a
)
+
[
p
(
b
)
]
2
Show that
a
=
b
a=b
a
=
b