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Simple and nice problem
Simple and nice problem
Source:
March 11, 2018
number theory
Problem Statement
a
,
b
a,b
a
,
b
are natural numbers such that
a
+
1
b
\frac{a+1}{b}
b
a
+
1
and
b
+
1
a
\frac{b+1}{a}
a
b
+
1
are integers.Let
d
=
G
C
D
(
a
;
b
)
d=GCD(a;b)
d
=
GC
D
(
a
;
b
)
.Prove that
d
2
≤
a
+
b
d^2\le a+b
d
2
≤
a
+
b
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