IIT JEE , AIEEE Forum - Mathematics , Trignometry

man111

(1) 111111111 up to1111 times.

when we divide this expression by 271

what will be the remainder.

sboosy

consider this way
1111(4 1's) divided by 270 Rem = 270
11111(5 1's) Rem = 0
111111(6 1's ) Rem= 1
(7 1's) Rem = 11
for 8 Rem = 111
for 9 Rem = 1111
for10Rem = 0
so similarly ....
for 15 Rem = 0
for 20 Rem = 0
.....
for 1110 Rem =0
so by pattern for 1111 Rem =1
that is 1111......(1111 times)
divided by 271 leaves 1 as remainder

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