Shell Script to Find Armstrong Numbers Between a Given Range

#!/bin/bash
# SCRIPT:  armstrong_bw_range.sh
# USAGE:   armstrong_bw_range.sh
# PURPOSE: Finding Armstrong numbers between given range.
#                         \\\\ ////
#                         \\ - - //
#                            @ @
#                    ---oOOo-( )-oOOo---
#Armstrong numbers are the sum of their own digits to the power of
#the number of digits. As that is a slightly brief wording, let me
#give an example:
#153 = 1³ + 5³ + 3³
#Each digit is raised to the power three because 153 has three
#digits. They are totalled and we get the original number again!
#Notice that Armstrong numbers are base dependent,but we'll mainly be
#dealing with base 10 examples.The Armstrong numbers up to 5 digits
#are 1 to 9,153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084
#
#####################################################################
#                     Script Starts Here                            #
#####################################################################

echo -n "Enter the Lower Limit : "
read Start
echo -n "Enter the Upper Limit : "
read Ending

echo "Armstrong Numbers between $Start and $Ending are: "

while [ $Start -le $Ending ]
do
     Number=$Start
     Length=${#Number}
     Sum=0
     OldNumber=$Number

     while [ $Number -ne  0 ]
     do
          Rem=$((Number%10))
          Number=$((Number/10))
          Power=$(echo "$Rem ^ $Length" | bc )
          Sum=$((Sum+Power))
     done

     if [ $Sum -eq $OldNumber ]
     then
         echo -n "$OldNumber  "
     fi

     let Start++
done
echo


OUTPUT:
# sh armstrong_bw_range.sh
Enter the Lower Limit : 1
Enter the Upper Limit : 500
Armstrong Numbers between 1 and 500 are:
1  2  3  4  5  6  7  8  9  153  370  371  407

# sh armstrong_bw_range.sh
Enter the Lower Limit : 1000
Enter the Upper Limit : 10000
Armstrong Numbers between 1000 and 10000 are:
1634  8208  9474