Question

ctr a=1+5+5^2+5^3+...+5^97+5^98 chia het cho 31

Answer 1

= ( 1 + 5 + 5^ 2 ) + ( 5^3 + 5^4 + 5^5 ) + ..............+ (5^96 +5^97 + 5^98 )

= 31 + 5^3 . (1 + 5 + 5^2) + ...............+ 5^96 . ( 1 + 5 + 5^2 )

= 31 + 5^ 3 . 31  + .............+ 5^96 . 31

= 31 . ( 1 + 5^3 +...+ 5^96)  chia hết cho 31

suy ra A chia hết ch 31

Answer 2

=

=[1+5+5² ] +[5³+5⁴+5⁵ ] +......+[5⁹⁶+5⁹⁷+5⁹⁸] 

=1*[1+5+5² ] +5³*[1+5+5²] + ..... +]  5⁹⁶*[1+5+5² ]

=1*31+5³*31+5⁶*31+.....+5⁹⁶*31
=31*[1+5³+5^6+.....+5⁹⁶ ] chia hết cho 31