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Given an nbit integer number a = a0a1a2 . . . an1 define a polynomial A(x) satisfying A(2) =a. How did we know which polynomial

Given an n−bit integer number a = a0a1a2 . . . an−1 define a polynomial A(x) satisfying A(2) =a.

How did we know which polynomial we have to define? After insert x=2, how to know it equals a?

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