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9
Number Theory problem
Number Theory problem
Source: Moldova TST 2018
April 6, 2018
number theory
number of divisors
Problem Statement
The positive integers
a
a
a
and
b
b
b
satisfy the sistem
{
a
10
+
b
10
=
a
a
11
+
b
11
=
b
\begin {cases} a_{10} +b_{10} = a \\a_{11}+b_{11 }=b \end {cases}
{
a
10
+
b
10
=
a
a
11
+
b
11
=
b
where
a
1
<
a
2
<
…
a_1 <a_2 <\dots
a
1
<
a
2
<
…
and
b
1
<
b
2
<
…
b_1 <b_2 <\dots
b
1
<
b
2
<
…
are the positive divisors of
a
a
a
and
b
b
b
. Find
a
a
a
and
b
b
b
.
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