A problem by OJAS JAIN
Level
pending
How many integer pairs (x,y) satisfy
The answer is 6.
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1 solution
By setting A = x − y , B = y we can put the original equation in the form ( A − 1 ) 2 + 3 ( B − 1 ) 2 = 1 2 . Since the only integer solutions of C 2 + 3 D 2 = 1 2 are ( C , D ) ∈ { ( 0 , ± 2 ) , ( ± 3 , ± 1 ) } , just six pairs of integers satisfy the original equation: ( − 2 , 0 ) , ( 0 , − 1 ) , ( 0 , 2 ) , ( 4 , 0 ) , ( 4 , 3 ) , ( 6 , 2 ) .