Question

Well there is this theorem,
( mathrm{a}^{wedge} mathrm{n}+mathrm{b}^{wedge} mathrm{n}+mathrm{c}^{wedge} mathrm{n}+mathrm{d}^{wedge} mathrm{n}+ldots ldots . /(mathrm{a}+mathrm{b}+mathrm{c}+mathrm{d}+ldots .) ) or a factor of ( (mathrm{a}+mathrm{b}+mathrm{c}+mathrm{d}+ldots .) ) leaves a
remainder 0 if ( n ) is odd and ( a, b, c, d, ldots ) is in AP.
here,
( 13+14+15+16=58 ) which is a multiple of 29,13,14,15,16 are in ( mathrm{AP} ) and 5 is odd ( , ) so
going by the theorem remainder is 0
Hope this helps.

# 26, What is the remainder, when 135 + 145 + 15% + 165 is divided by 29? roncon A

Solution