Determine at least three pairs of positive integers (x,y) with x< y such that xy(x+y) is not divisible by 7, but (x+y)^{7} - x^{7} - y^{7} is divisible by 7^{7}

Does the given problem generate an infinite number of pairs as solutions?

*Can you do this in a short time using pen and paper, and eventually a hand calculator, but no computer programs?*

(In reply to

re: Hint by Dej Mar)

True.

However, at the precise time of its publication ( 2007-04-18); I distinctly remember having observed (x+y)^7 - x^7 - y^7 in the problem text.

Accordingly, this seems to be a temporary database error; and I have sought assistance of The Director (Levik) to restore the problem text.

[Edit] The problem text is now restored to its original form.

*Edited on ***April 19, 2007, 3:01 pm**