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 Four Egyptian Fractions (Posted on 2013-11-13)
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 No Rating

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 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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