When, recently, I did a conversion of a positive integral Celsius temperature, C = 275, to its Fahrenheit equivalent, it turned out to be F = 527, and I notice that I could have simply moved the digit at right of C, to the front, to obtain F. After some intense calculations, I failed to discover the next largest such example.

Does one exist, and if so, what is it?

(In reply to re: I think I found one! (I didn't) by Bob Smith)

(5*10^Z - 41) mod 17 = 0

when Z = 2 or 18 or 34 ...

In UBASIC:

   10   for N=1 to 40
   20    Rslt=(5*10^N-41)@17
   30    print N,Rslt
   40   next
run
 1       9
 2       0
 3       12
 4       13
 5       6
 6       4
 7       1
 8       5
 9       11
 10      3
 11      8
 12      7
 13      14
 14      16
 15      2
 16      15
 17      9
 18      0
 19      12
 20      13
 21      6
 22      4
 23      1
 24      5
 25      11
 26      3
 27      8
 28      7
 29      14
 30      16
 31      2
 32      15
 33      9
 34      0
 35      12
 36      13
 37      6
 38      4
 39      1
 40      5

Posted by Charlie on 2005-08-31 19:34:59