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Saint Petersburg Mathematical Olympiad
2015 Saint Petersburg Mathematical Olympiad
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Interesting primes
Interesting primes
Source: St Petersburg Olympiad 2015, Grade 11, P2
October 17, 2017
number theory
Problem Statement
a
,
b
>
1
a,b>1
a
,
b
>
1
- are naturals, and
a
2
+
b
,
a
+
b
2
a^2+b,a+b^2
a
2
+
b
,
a
+
b
2
are primes. Prove
(
a
b
+
1
,
a
+
b
)
=
1
(ab+1,a+b)=1
(
ab
+
1
,
a
+
b
)
=
1
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