3 votes 3 votes Compute $2^{32} \; \mod \; 37$ Quantitative Aptitude goclasses_wq1 numerical-answers goclasses quantitative-aptitude number-system modular-arithmetic remainder-theorem 1-mark + – GO Classes asked May 1, 2022 GO Classes 603 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply ankitgupta.1729 commented Aug 14, 2022 reply Follow Share $2^{-4} \ 2^{36} \mod 37 = 2^{-4} \mod 37$ (By Fermat’s Little Theorem) Since, $2 \times 19 \equiv 1 \mod 37. \ $ So, $2^{-1} \mod 37 = 19$ Hence, $2^{-4} \mod 37 = 19^4 \mod 37 = 7$ 0 votes 0 votes ankitgupta.1729 commented Aug 14, 2022 reply Follow Share $2^{-4} \mod 37 = 16^{-1} \mod 37$ Using Euclidean Algorithm $37 = 2*16 + 5$ and $16 = 3*5 + 1 \Rightarrow 1 = 16 \ – \ 3*(37 \ – \ 2*16) \Rightarrow 1 = 7*16 \ – \ 3*37$ Hence, $16^{-1} \mod 37 = 7$ 0 votes 0 votes MrBibek commented Sep 13, 2022 reply Follow Share Hello sir @ankitgupta.1729 where can i learn the above approaches? 0 votes 0 votes ankitgupta.1729 commented Sep 14, 2022 reply Follow Share Fermat’s Little Theorem Extended Euclidean Algorithm These are quite famous, so, if you don’t get it from here then you can search some text over web or videos on youtube also. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes $2^2\equiv 4\; \mod \; 37\\ 2^4 \equiv 16 \; \mod \; 37\\ 2^8 \equiv 256 \equiv 34 \; \mod \; 37\\ 2^{16} \equiv (-3)^2 \equiv 9 \; \mod \; 37\\ 2^{32} \equiv 81 \; \mod \; 37\\ 2^{32} \equiv 7 \; \mod \; 37$ GO Classes answered May 1, 2022 edited May 1, 2022 by Lakshman Bhaiya GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Ans: 7 Jay Patel 009 answered Mar 14, 2023 Jay Patel 009 comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Same as : https://gateoverflow.in/374789/go-classes-weekly-quiz-1-general-aptitude-question-2 Udhay_Brahmi answered Aug 14, 2022 Udhay_Brahmi comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes To calculate 2³² mod 37=(2⁸)⁴ mod 37 = (256)⁴ mod 37 =(256 mod 37)⁴ mod 37=(-3)⁴ mod 37 = 81 mod 37 = 77 is the answer. ravi2002 answered Feb 20 ravi2002 comment Share Follow See all 0 reply Please log in or register to add a comment.