Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
Sign in
Please select an account to continue using cracku.in
↓ →
Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
State True or False. $$2^{2^{2011}} + 1$$ divides $$2^{2^{2012}} - 1$$
Correct Answer: True
Since $$2^{2012} = 2 \times 2^{2011}$$, $$2^{2^{2012}} - 1 = \left(2^{2^{2011}}\right)^2 - 1 = \left(2^{2^{2011}} - 1\right)\left(2^{2^{2011}} + 1\right)$$. So $$2^{2^{2011}} + 1$$ is a factor, and the statement is True.
Was this solution helpful?
Predict your JEE Main percentile, rank & performance in seconds
Educational materials for JEE preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.