The Integer Problem
Find all positive integers satisfying the expression below:
Type as the answer.
The answer is 2.
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1 solution
Rewriting, the equation is
4 x y − 2 x − 2 y + 1 = 1
The left-hand side of this factorises, giving
( 2 x − 1 ) ( 2 y − 1 ) = 1
The only way the product of two integers can be 1 is if they are both − 1 or both 1 . This gives ( 0 , 0 ) and ( 1 , 1 ) as the only possible integer solutions. We can discount the first of these as we are only looking for positive integer solutions; hence the answer is 1 + 1 = 2 .