MathCastle
Proof WritingHardInduction

Induction · Hard problem

To prove 7∣32n−2n7 \mid 3^{2n} - 2^n for all n≥0n \ge 0, the step writes 32k+2−2k+1=9(32k−2k)+c⋅2k3^{2k+2} - 2^{k+1} = 9(3^{2k} - 2^k) + c\cdot2^k. What is cc?