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4. (i) Show that the polynomial x4 + x + 1 has no integer roots, but that it has a root modulo 3, and

4. (i) Show that the polynomial x4 + x + 1 has no integer roots, but that it has a root modulo 3, and factorise it over Z3. (ii) Show that the equation 7x 6x + 2x 1 = 0 has no integer solutions.

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