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Raise to the seventh power, get factor (Posted on 2007-04-18) Difficulty: 5 of 5
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 - x7 - y7 is divisible by 77

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?

See The Solution Submitted by K Sengupta    
Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Hint | Comment 4 of 5 |
(In reply to re: Hint by Dej Mar)


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
  Posted by K Sengupta on 2007-04-19 04:20:47

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