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The abc Arithmetics
(solution)

The formula which helps to find such pairs is derived from the simple equality that a + b = a x b. From this we have that b always equals a/(a-1). The formula shows there is an infinity number of such pairs existing.

Thus if a is 3 then according to that formula above b is 1.5. When they are multiplied the result is the same as when they are added together. It is 4.5 as shown in the illustration.

 
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Last Update
October 26, 2003

 
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