perplexus.info :: Numbers : Elegant Exponent Exposition II

Elegant Exponent Exposition II (Posted on 2010-12-04)

Each of the capital letters in bold denotes a different base ten digit from 1 to 9 in this cryptarithmetic expression:

A^B/C + D^E/F + G^H/I

(I) Determine the respective smallest and the largest positive integer that this expression can assume.

(II) Determine the respective smallest and the largest prime number that this expression can assume. What are the respective smallest and the largest palindrome assumed by the above expression?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(i) The respective smallest and the largest integer the expression can assume are respectively 8 and 134217881.
2(a) The respective smallest and the largest prime number the expression can assume are respectively 13 and 5,764,907.
2(b) The respective smallest and the largest palindrome the expression can assume are respectively 77 and 33,033.
For an explanation, refer to the solution submitted b Charlie here and here, and here.

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

Subject	Author	Date
re(2): computer solution for integers and primes -- now palindromes	Charlie	2010-12-04 20:06:26
re: computer solution for integers and primes -- now palindromes	Charlie	2010-12-04 19:55:33
computer solution for integers and primes	Charlie	2010-12-04 18:26:37

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