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Four Egyptian Fractions (Posted on 2013-11-13) Difficulty: 2 of 5
Find positive integer solutions to the equation 1/a + 1/b + 1/c + 1/d = 1
(a ≤ b ≤ c ≤ d). How many solutions exist?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution computer solution Comment 6 of 6 |

After much debugging:

list
   10   A=2
   20   while 4//A>=1
   30      B=A
   40      while 1//A+3//B>=1
   50       C=B
   55       if 1//A+1//B<1 then
   60        :while 1//A+1//B+2//C>=1
   70           :D=C
   74           :if 1//A+1//B+1//C<1 then
   75            :while 1//A+1//B+1//C+1//D>=1
   80             :if 1//A+1//B+1//C+1//D=1 then
   90              :print A;B;C;D
   94             :endif
   95             :inc D
   96            :wend
   99           :endif
  100           :inc C
  110        :wend
  120        inc B
  130      wend
  140      inc A
  150   wend
OK
run
 2  3  7  42
 2  3  8  24
 2  3  9  18
 2  3  10  15
 2  3  12  12
 2  4  5  20
 2  4  6  12
 2  4  8  8
 2  5  5  10
 2  6  6  6
 3  3  4  12
 3  3  6  6
 3  4  4  6
 4  4  4  4
OK


  Posted by Charlie on 2013-11-13 16:18:04
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