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Proof WritingChallengeExistence, Uniqueness and Counterexamples

Existence, Uniqueness and Counterexamples · Challenge problem

Division with remainder is unique because 0≤r<70 \le r < 7 in n=7q+rn = 7q + r. Suppose the condition were weakened to 0≤r≤70 \le r \le 7. How many nn in {1,2,…,100}\{1, 2, \ldots, 100\} would then have TWO representations?