(New page: ''' Does anyone know why x^4 + 1 is reducible mod p for any prime. Is this because x^4 + 1 mod 3 has 2*4 + 1 = 9 mod 3 = 0??? Because 0^4 + 1 = 1, 1^4 + 1 = 2, 2^4 + 1 = 17 do not seem to ...) |
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Is this because x^4 + 1 mod 3 has 2*4 + 1 = 9 mod 3 = 0??? | Is this because x^4 + 1 mod 3 has 2*4 + 1 = 9 mod 3 = 0??? | ||
Because 0^4 + 1 = 1, 1^4 + 1 = 2, 2^4 + 1 = 17 do not seem to be 0 mod 3.''' | Because 0^4 + 1 = 1, 1^4 + 1 = 2, 2^4 + 1 = 17 do not seem to be 0 mod 3.''' | ||
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| + | Irreducibility for degree 4 or higher does not have to have zeros. | ||
| + | Ex (x^2 + 1)^2 = x^4 + 2x^2 + 1 | ||
Latest revision as of 14:01, 17 December 2008
Does anyone know why x^4 + 1 is reducible mod p for any prime. Is this because x^4 + 1 mod 3 has 2*4 + 1 = 9 mod 3 = 0??? Because 0^4 + 1 = 1, 1^4 + 1 = 2, 2^4 + 1 = 17 do not seem to be 0 mod 3.
Irreducibility for degree 4 or higher does not have to have zeros. Ex (x^2 + 1)^2 = x^4 + 2x^2 + 1
