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Switzerland Team Selection Test
2019 Switzerland Team Selection Test
2
2
Part of
2019 Switzerland Team Selection Test
Problems
(1)
Prime Expressible in Root of a Rational
Source: Swiss TST 2019 P2
5/12/2020
Find the largest prime
p
p
p
such that there exist positive integers
a
,
b
a,b
a
,
b
satisfying
p
=
b
2
a
−
b
a
+
b
.
p=\frac{b}{2}\sqrt{\frac{a-b}{a+b}}.
p
=
2
b
a
+
b
a
−
b
.
number theory
prime numbers