The number of integer pairs (x,y) satisfy the equation #x(x+1)=2^y# is?

1 Answer
P dilip_k
Jul 26, 2018

If #x# is an intger then #x(x+1)# is a product of two consecutive integers . One of which is odd and other is even. Again the #2^y#,where #y# is an integer has the values #2,4,8,16...#.

So #2^y# has no multiple of odd intger other than 1.

Hence the given relation #x(x+1)=2^y# is satisfied only when #x=1 and y=1#.

So the number of required intger pairs is ONE.

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