[JEE Advanced 1996] prove by induction that for every integer n 1 3 2n 1 is divisible
Prove by induction that for every integer $n\ge1$, $3^{2n}-1$ is divisible by $2^{n+2}$ but not by $2^{n+3}$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
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· 2d ago
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Answer: Proved.
$3^{2n}-1=(3^{2^{... }})$… write $3^{2n}-1=(3^n-1)(3^n+1)$; the $2$-adic valuation of $3^{2n}-1$ is exactly $n+2$ (lifting-the-exponent), so divisible by $2^{n+2}$ but not $2^{n+3}$.
JEE Advanced 1996 · Binomial Theorem — verified solution by the Vidaara Team.
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