Please amswer ASAP , its urgent . what will be the remainder when #[{7^365-1}/6]# is divided by 5? i know that the divident will be a whole number so plz just write numeric value of answer . i need to confirm..

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Answer 1 · 2017-12-11T15:22:13

#1#

Note that modulo #5#:

#7^(4n+0) -= 1#

#7^(4n+1) -= 2#

#7^(4n+2) -= 4#

#7^(4n+3) -= 3#

and:

#(7^365-1)/6 = (7^365-1)/(7-1) = sum_(k=0)^364 7^k#

Now:

#1+2+4+3 -= 0#

So:

#sum_(k=0)^364 7^k = sum_(k=0)^90 (7^(4k+0)+7^(4k+1)+7^(4k+2)+7^(4k+3)) + 7^364 -= 0+1 = 1#

Or more simply:

#(7^365-1)/6 -= (7^(4(color(blue)(91))+1)-1)/1 -= (2-1)/1 = 1#