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Consider the following computation done in Z11. What is 2-1 + 3-1 + 4-1 +5-1=? that is 2⁻¹+3⁻¹+4⁻¹+5⁻¹=?

1 Answer

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Final answer:

In Z11, the computation 2^(-1) + 3^(-1) + 4^(-1) + 5^(-1) is equal to 0.

Step-by-step explanation:

In Z11, to find the inverse of a number, we need to find a number such that when multiplied by the original number, the result is congruent to 1 modulo 11.

For example:

The inverse of 2 is 6, because 2*6 = 12 is congruent to 1 modulo 11.

The inverse of 3 is 4, because 3*4 = 12 is congruent to 1 modulo 11.

The inverse of 4 is 3, because 4*3 = 12 is congruent to 1 modulo 11.

The inverse of 5 is 9, because 5*9 = 45 is congruent to 1 modulo 11.

Therefore, the computation 2^(-1) + 3^(-1) + 4^(-1) + 5^(-1) is equal to 6 + 4 + 3 + 9 = 22 modulo 11.

Since 22 is congruent to 0 modulo 11, the final answer is 0.

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