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Duplicate Digit Determination III (Posted on 2010-12-23)

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

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(i) minimum of x+y =106, with x=3 and y=103
(ii) minimum of x+y = 508, with x=4 and y= 504
For an explanation, refer to the solution submitted by Charlie in this location.

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

	Subject	Author	Date
	computer solution	Charlie	2010-12-23 15:29:58

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