perplexus.info :: Just Math : Duplicate Digit Determination IV

Duplicate Digit Determination IV (Posted on 2011-06-05)

(I) Each of x and y is a positive integer with x < y such that, reading from left to right, the first two 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 three digits in the 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.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(i) Minimum of x+y =29, with x=1, and y=28.
(ii) Minimum of x+y =61, with x=17, and y=44.
For an explanation, refer to the solution submitted by Brian Smith in this location.

Comments: ( You must be logged in to post comments.)

	Subject	Author	Date
	Solution	Brian Smith	2017-07-02 14:14:56

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