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The cunning Condition (Posted on 2013-08-25) Difficulty: 3 of 5
Find necessary and sufficient conditions for the positive integer triple(A,B,C)to satisfy:


No Solution Yet Submitted by Danish Ahmed Khan    
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full solution Comment 5 of 5 |
start with the given equation
factor the numerator and denominator on the left side
cancel out the common terms on both sides
bring denominator over to the left side
shuffle equation
this holds identically if b=c so that is one set of solutions.
If b!=c, then we can divide out the b-c terms on both sides to get
which is the other set of solutions.

Thus all solutions are given by

  Posted by Daniel on 2013-08-25 18:03:26
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