Let x be an ODD integer show that for n>=3

x^2^(n-2) is congruent to 1 (mod 2^n)

Sorry about the superscripts I dont use the computer for math often.

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- Nov 3rd 2009, 06:34 PMstumped765congruence modulo 2^n
Let x be an ODD integer show that for n>=3

x^2^(n-2) is congruent to 1 (mod 2^n)

Sorry about the superscripts I dont use the computer for math often. - Nov 3rd 2009, 06:47 PMBruno J.
It holds for ; I'll let you prove that. Suppose it holds up to . Note that ; and by the induction hypothesis, is divisible by , and since is odd, is divisible by 2 so is divisible by .