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2024 Iran MO (2nd Round)
3
Another Number Theory!
Another Number Theory!
Source: Iran MO 2024 second round P6
April 19, 2024
number theory
Problem Statement
Find all natural numbers
x
,
y
>
1
x,y>1
x
,
y
>
1
and primes
p
p
p
that satisfy
x
2
−
1
y
2
−
1
=
(
p
+
1
)
2
.
\frac{x^2-1}{y^2-1}=(p+1)^2.
y
2
−
1
x
2
−
1
=
(
p
+
1
)
2
.
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