Each of P, Q, R, and S is a positive integer with P<Q<R<S.
Find the quadruplets (P, Q, R, S) that satisfy this equation:
1/P + 1/Q + 1/R + 1/S = 1
Prove that these are the only possible quadruplets that satisfy the given conditions.
Note: Computer program solutions are welcome, but a semi-analytical solution is preferred.
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Submitted by K Sengupta
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Rating: 5.0000 (1 votes)
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Solution:
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(P, Q, R, S) = (2, 4, 5, 20), (2, 4, 6, 12), , (2, 3, 7, 42) , (2, 3, 8, 24), (2, 3, 9, 18), and (2, 3, 10, 15) are the required solutions to the given puzzle.
For an explanation, refer to the analytic solution submitted by H M in this location. |
