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Spain Mathematical Olympiad
1996 Spain Mathematical Olympiad
1
1
Part of
1996 Spain Mathematical Olympiad
Problems
(1)
if \frac{a+1}{b}+ \frac{b+1}{a} is integer then gcd(a,b)<=\sqrt{a+b}
Source: Spanish Mathematical Olympiad 1996 P1
7/31/2018
The natural numbers
a
a
a
and
b
b
b
are such that
a
+
1
b
+
b
+
1
a
\frac{a+1}{b}+ \frac{b+1}{a}
b
a
+
1
+
a
b
+
1
is an integer. Show that the greatest common divisor of a and b is not greater than
a
+
b
\sqrt{a+b}
a
+
b
.
number theory
greatest common divisor
Integer