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Contests
National and Regional Contests
PEN Problems
PEN P Problems
19
19
Part of
PEN P Problems
Problems
(1)
P 19
Source:
5/25/2007
Let
n
n
n
be an integer of the form
a
2
+
b
2
a^2 + b^2
a
2
+
b
2
, where
a
a
a
and
b
b
b
are relatively prime integers and such that if
p
p
p
is a prime,
p
≤
n
p \leq \sqrt{n}
p
≤
n
, then
p
p
p
divides
a
b
ab
ab
. Determine all such
n
n
n
.
number theory
relatively prime
Additive Number Theory