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P2
Romania Junior TST 2021 Day 1 P2
Romania Junior TST 2021 Day 1 P2
Source:
May 16, 2021
number theory
prime numbers
Romanian TST
TST
Problem Statement
Find all the pairs of positive integers
(
x
,
y
)
(x,y)
(
x
,
y
)
such that
x
≤
y
x\leq y
x
≤
y
and
(
x
+
y
)
(
x
y
−
1
)
x
y
+
1
=
p
,
\frac{(x+y)(xy-1)}{xy+1}=p,
x
y
+
1
(
x
+
y
)
(
x
y
−
1
)
=
p
,
where
p
p
p
is a prime number.
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