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2004 Korea Junior Math Olympiad
3
3
Part of
2004 Korea Junior Math Olympiad
Problems
(1)
Multiples of p expressable as
Source: 2004 Korea Junior Math Olympiad
6/28/2024
For an arbitrary prime number
p
p
p
, show that there exists infinitely many multiples of
p
p
p
that can be expressed as the form
x
2
+
y
+
1
x
+
y
2
+
1
\frac{x^2+y+1}{x+y^2+1}
x
+
y
2
+
1
x
2
+
y
+
1
Where
x
,
y
x, y
x
,
y
are some positive integers.
number theory
prime numbers
multiple