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0571 number theory 5th edition Round 7 p1

Source:

May 6, 2021
number theory5th edition

Problem Statement

Prove that the numbers (2n1i),i=0,1,...,2n11,{{2^n-1} \choose {i}}, i = 0, 1, . . ., 2^{n-1} - 1, have pairwise different residues modulo 2n2^n