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Problem 1
QM(a,b)|AM(a,b) implies a=b (Serbia MO 2005 2nd Grade P1)
QM(a,b)|AM(a,b) implies a=b (Serbia MO 2005 2nd Grade P1)
Source:
April 11, 2021
power mean
Divisibility
algebra
number theory
Problem Statement
Let
a
a
a
and
b
b
b
be positive integers and
K
=
a
2
+
b
2
2
K=\sqrt{\frac{a^2+b^2}2}
K
=
2
a
2
+
b
2
,
A
=
a
+
b
2
A=\frac{a+b}2
A
=
2
a
+
b
. If
K
A
\frac KA
A
K
is a positive integer, prove that
a
=
b
a=b
a
=
b
.
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