Determine all possible five digit positive decimal (base 10) integer(s) of the form abbbb, with a ≠ b, that contain no leading zeroes, such that (abbbb² - 1) is equal to a positive ten digit integer (with no leading zeroes) containing each of the digits 0 to 9 exactly once.

Note: While the solution may be trivial with the aid of a computer program, show how to derive it without one.

  100   for A=1 to 9
  200     for B=0 to 9
  300       if A<>B then
  400         :Tst=10000*A+1111*B:tst1=tst
  500         :Tst=Tst*Tst-1
  600         :Tsts=cutlspc(str(Tst))
  700         :if len(Tsts)=10 then
  800           :Good=1
  900           :for I=1 to 9
 1000             :if instr(mid(Tsts,I+1,*),mid(Tsts,I,1)) then Good=0:endif
 1100           :next
 1200           :if Good then print Tst1,tst
 1300     next B
 1400   next A

giving

 85555   7319658024
 97777   9560341728

Posted by Charlie on 2008-08-17 13:35:13