MathDB
Problems
Contests
National and Regional Contests
Spain Contests
Spain Mathematical Olympiad
2003 Spain Mathematical Olympiad
Problem 2
Problem 2
Part of
2003 Spain Mathematical Olympiad
Problems
(1)
2003 National Spain Olympiad, Problem 2
Source: 2003 National Spain Olympiad
6/1/2017
Does there exist such a finite set of real numbers
M
{M}
M
that has at least two distinct elements and has the property that for two numbers,
a
{a}
a
,
b
{b}
b
, belonging to
M
{M}
M
, the number
2
a
ā
b
2
{2a - b^2}
2
a
ā
b
2
is also an element in
M
{M}
M
?
sets of integers
number theory