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!Fancy sequence

Author: anonymous
Problem has been solved: 6 times

Русский язык | English Language

We call a sequence $ Fancy $ if it consists only of digits and when summing all its elements, we get a number whose last digit does not occur among the elements of this sequence. Let $ x $ be the number of ordered $ Fancy $ sequences consisting of 666 elements. It is known that $ x $ can be represented in the form $ a^2 + b^2 $, for some positive integers $ a $ and $ b $ such that $ b $ takes the smallest possible value. Find the number of natural divisors of $ ab $.

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