(I) Each of x and y is a positive integer with x < y such that, reading from left to right, the first four digits in the base ten expansions of 1978^x and 1978^y are congruent.

Determine the minimum value of x+y.

(II) What is the minimum value of x+y - if, keeping all the other conditions in (i) unaltered, the first five digits in the respective base ten expansions of 1978^x and 1978^y are congruent?

Note: None of the expansions of 1978^x and 1978^y can contain any leading zero

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Posted by Hedda Dunn on 2024-12-10 12:01:29