program Prob1104;
const
  maxn=1000000;
var
  n,low,k,r,i:longint;
  a:array [1..maxn] of shortint;
  ch:char;
begin
  assign(input,'');
  assign(output,'');
  reset(input);
  n:=0;
  low:=0;
  while not eoln do
  begin
    read(ch);
    if ch<>' ' then
    begin
      inc(n);
      if ch in ['0'..'9']
        then a[n]:=ord(ch)-48
        else a[n]:=ord(ch)-55;
      if a[n]+1>low then low:=a[n]+1;
    end;
  end;
  close(input);

  if low<2 then low:=2;
  for k:=low to 36 do
  begin
    r:=0;
    for i:=1 to n do
    begin
      r:=r*k+a[i];
      r:=r mod (k-1);
    end;
    if r=0 then
    begin
      rewrite(output);
      writeln(k);
      close(output);
      halt;
    end;
  end;

  rewrite(output);
  writeln('No solution.');
  close(output);
end.

You got Memory Limit Exceed because you use an 1 Mb array
(max memory limit for this task) and you dont have any other
Memory available for your program.
I use only 17 bytes of variables and they report 373 Kb of
memory used