Question
Mon April 13, 2015 By: Madhuri Kulkarni

what is method of solving the question-'whether 6 to the power of n is divisible by 5'?

Expert Reply
Vimala Ramamurthy
Wed April 15, 2015
L e t space u s space p r o v e space t h i s space b y space t h e space m e t h o d space o f space i n d u c t i o n. W h e n space n equals 1 comma space 6 to the power of 1 equals 6 space a n d space 6 minus 1 equals 5 space i s space d i v i s i b l e space b y space 5 L e t space u s space a s s u m e space t h a t space 6 to the power of n minus 1 space i s space d i v i s i b l e space b y space 5 comma space w h e r e space n equals k T h u s comma 6 to the power of k minus 1 space i s space d i v i s i b l e space b y space 5 W e space n e e d space t o space p r o v e space t h a t comma space 6 to the power of n minus 1 space i s space d i v i s i b l e space b y space 5 comma space w h e r e space n equals k plus 1 T h a t space i s space w e space n e e d space t o space p r o v e space t h a t comma space 6 to the power of k plus 1 end exponent minus 1 space i s space d i v i s i b l e space b y space 5. C o n s i d e r comma space 6 to the power of k plus 1 end exponent minus 1 equals 6 to the power of k times 6 minus 1 space space space space space space space space space space space space space equals 6 to the power of n times 6 minus 6 plus 5 space space space space space space space space space space space space space equals 6 open parentheses 6 to the power of k minus 1 close parentheses plus 5 space space space space space space space space space space space space space equals 6 open parentheses 5 m close parentheses plus 5 space space space space space space space space space space open square brackets because space 6 to the power of k space i s space d i v i s i b l e space b y space 5 close square brackets space space space space space space space space space space space space space equals 5 open parentheses 6 m close parentheses plus 5 space space space space space space space space space space space space space space equals 5 open parentheses 6 m plus 1 close parentheses H e n c e space i t space i s space c l e a r space t h a t space 6 to the power of k plus 1 end exponent minus 1 space i s space d i v i s i b l e space b y space 5 rightwards double arrow space 6 to the power of n minus 1 space i s space d i v i s i b l e space b y space 5 comma space f o r space a l l space n element of N rightwards double arrow space 6 to the power of n space i s space n o t space d i v i s i b l e space b y space 5 comma space f o r space a l l space n element of N
Home Work Help