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?

(In reply to computer solution for integers and primes by Charlie)

the added code:

100           :spal=cutspc(str(sum))
110           :pal=1
120           :for i=1 to int(len(spal))
130              :if mid(spal,i,1)<>mid(spal,len(spal))+1-i,1) then pal=0:endif
140           :next
150           :if pal=1 and sum<lowpal then lowpal=sum:lowpalstr=s$:endif
155           :if pal=1 and sum>highpal then highpal=sum:highpalstr=s$:endif

finds

157263948        8
693742851        33033

where 693742851 represents 6^(9/3)+7^(4/2)+8^(5/1), which equals the largest palindrome: 33033.

Posted by Charlie on 2010-12-04 19:55:33