MathCastle
Proof Writing & Problem SolvingEasy

Proof Writing & Problem Solving · Easy problem

A proof that n2n^2 leaves remainder 11 on division by 33 whenever 3∤n3 \nmid n treats the case n=3k−1n = 3k - 1 by writing n2=9k2−6k+1=3(3k2−2k)+1n^2 = 9k^2 - 6k + 1 = 3(3k^2 - 2k) + 1. For n=14n = 14, what is 3k2−2k3k^2 - 2k?

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