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find all triples (a,b,c) of positive integers such that (1+1/a)(1+1/b)(1+1/c)=3

find all triples (a,b,c) of positive integers such that (1+1/a)(1+1/b)(1+1/c)=3

Grade:12th pass

1 Answers

Rishit Dagli
28 Points
5 years ago
Let 
1+1/a = x
1+1/b = y
1+1/c = z
As 3 is a prime number it's factors are (3,1)
Therefore,
(x,y,z) = (1,1,3)(1,3,1)(3,11) as positive integers are asked
Case 1:
As 1 divided by any integer cannot give answer as 0 
There are no positive integral solution sets
 
Hope it helps
Rishit Dagli

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