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From: jm bergot on 15 Jun 2010 15:59
Take the coprimes of 16 and divide them into 16. You
get 0,1,1,2,7,5,3,1 with sum 20. Take all the squares
of the coprimes {1,3,5,7,9,11,13,15} and find the sum of
the remainders when divided by 16. You get 1,9,9,1,1,9,9,1 with sum 40. The above 20 divides this
40.
(a)Does this happen with other powers of 2?
(b)Does this happen with any other numbers?
(c)Any other squares?
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