Does , n natural, have odd solutions in the naturals for x? How do you know (does Euler's theorem tell me this)?
Last edited by sleepingcat; Jun 7th 2008 at 05:34 PM.
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Originally Posted by sleepingcat Does have odd solutions in the naturals? How do you know? All odd natural numbers (n) can be written For the above to have solutions in the odd naturals this must be true for some k but mod 3 This false so there is not a solution.
Originally Posted by sleepingcat Does , n natural, have odd solutions in the naturals for x? How do you know (does Euler's theorem tell me this)? Note that (this identity appears in The Elements). Next, . Thus, (depending whether is even or odd). Thus, it is impossible to have this congruent to mod 3.
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