Show that the congruence x^2≡1 (mod 2^k) has exactly four incongruent solutions, namely x≡(+-)1 or (+-)(1+2^(k-1)) (mod 2^k), when k>2. Show that when k=1 there is one solution and that when k=2 there are two incongruent solutions.

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- Oct 13th 2010, 08:23 PMalice8675309incongruent solutions
Show that the congruence x^2≡1 (mod 2^k) has exactly four incongruent solutions, namely x≡(+-)1 or (+-)(1+2^(k-1)) (mod 2^k), when k>2. Show that when k=1 there is one solution and that when k=2 there are two incongruent solutions.

- Oct 16th 2010, 07:27 PMchiph588@