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help on gcd(x,y) = x xor y
By yaptrick, history, 23 hours ago, In English

hi,

could anyone help me with the following problem?

find the number of pairs (x,y) for which 1<=x,y<=10^7 and gcd(x,y) = x xor y

here are my thoughts: we can let x=da and y=db for coprime a,b then we must have a XOR b = 1 i.e. a and b are consecutive integers. how do we proceed from here

thanks!

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23 hours ago, # |
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sorry :(

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23 hours ago, # |
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here

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23 hours ago, # |
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probably $$$O(n ~log~ n)$$$ soln

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    23 hours ago, # ^ |
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    oops i miscalculated, apparently da xor db does not necessarily equal d(a xor b). thanks for the help though

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10 hours ago, # |
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seems no solution lower than $$$O(n\log n)$$$?

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