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2n 3. Let a be an odd integer. Prove by induction that a²" - 1 is divisible by 2n+1 for every integer n ≥ 0.

2n 3. Let a be an odd integer. Prove by induction that a²" - 1 is divisible by 2n+1 for every integer n ≥ 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Problem 3:** Let \( a \) be an odd integer. Prove by induction that \( a^{2^n} - 1 \) is divisible by \( 2^{n+1} \) for every integer \( n \geq 0 \).
Transcribed Image Text:**Problem 3:** Let \( a \) be an odd integer. Prove by induction that \( a^{2^n} - 1 \) is divisible by \( 2^{n+1} \) for every integer \( n \geq 0 \).
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