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Austrian-Polish
1998 Austrian-Polish Competition
7
7
Part of
1998 Austrian-Polish Competition
Problems
(1)
a^ab^b has exactly 98 zeros
Source: Austrian - Polish 1998 APMC
5/4/2020
Consider all pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of natural numbers such that the product
a
a
b
b
a^ab^b
a
a
b
b
written in decimal system ends with exactly
98
98
98
zeros. Find the pair
(
a
,
b
)
(a, b)
(
a
,
b
)
for which the product
a
b
ab
ab
is the smallest.
number theory
Digits