How do you express a fraction like this using modular numbers? Help!
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There are only two elements in Z2: 0 and 1. Of these, 0 has no inverse and 1 is its own inverse.
Since 3 = 1 (mod 2), it follows that
3^-1 = 1^-1 = 1 (mod 2).
On the other hand, something like 1/2 is nonsense in Z2, since 2 = 0 (mod 2). Instead, we would write
2x^3 + x + 1 = x + 1
over Z2. Then it's already monic.
Since 3 = 1 (mod 2), it follows that
3^-1 = 1^-1 = 1 (mod 2).
On the other hand, something like 1/2 is nonsense in Z2, since 2 = 0 (mod 2). Instead, we would write
2x^3 + x + 1 = x + 1
over Z2. Then it's already monic.
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2|x-(1/3) = {1/3, 7/3, 10/3....}