Determine all possible positive base ten repdigit(s) N, such that the sum of the digits of N² is equal to 37.

(In reply to re: computer solution (a quibble) by Steve Herman)

list
   10   for Rd=1 to 9
   20      N=Rd
   30      loop
   40        N2=N*N:N2s=cutspc(str(N2))
   45        T=0
   50        for I=1 to len(N2s)
   60         T=T+val(mid(N2s,I,1))
   70        next
   80        if T=37 then print N,N2
   90        N=10*N+Rd
  100        if N>9999999999999999999999999999999999999999999999 then goto 120
  110      endloop
  120   next
  200   end
OK
run
 2222    4937284
 7777    60481729
OK

 

Posted by Charlie on 2009-06-04 16:34:03