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Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1974 Swedish Mathematical Competition
3
3
Part of
1974 Swedish Mathematical Competition
Problems
(1)
last two digits of a_9=9^{a_8}
Source: 1974 Swedish Mathematical Competition p3
3/26/2021
Let
a
1
=
1
a_1=1
a
1
=
1
,
a
2
=
2
a
1
a_2=2^{a_1}
a
2
=
2
a
1
,
a
3
=
3
a
2
a_3=3^{a_2}
a
3
=
3
a
2
,
a
4
=
4
a
3
a_4=4^{a_3}
a
4
=
4
a
3
,
…
\dots
…
,
a
9
=
9
a
8
a_9 = 9^{a_8}
a
9
=
9
a
8
. Find the last two digits of
a
9
a_9
a
9
.
number theory
recurrence relation
last digits
Digits