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Problems
Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2004 Junior Balkan Team Selection Tests - Moldova
4
4
Part of
2004 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
max {a_1, a_2,. . . , a_{12} } - min {a_1, a_2,. . . , a_{12}\} = 20
Source: 2004 Moldova JBMO TST p4
2/20/2021
Different non-zero natural numbers a
1
,
a
2
,
.
.
.
,
a
12
_1, a_2,. . . , a_{12}
1
,
a
2
,
...
,
a
12
satisfy the condition: all positive differences other than two numbers
a
i
a_i
a
i
and
a
j
a_j
a
j
form many
20
20
20
consecutive natural numbers. a) Show that
max
{
a
1
,
a
2
,
.
.
.
,
a
12
}
−
min
{
a
1
,
a
2
,
.
.
.
,
a
12
}
=
20
\max \{a_1, a_2,. . . , a_{12}\} - \min \{a_1, a_2,. . . , a_{12}\} = 20
max
{
a
1
,
a
2
,
...
,
a
12
}
−
min
{
a
1
,
a
2
,
...
,
a
12
}
=
20
. b)Determine
12
12
12
natural numbers with the property from the statement.
number theory
consecutive