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.
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.