Can u solve? Part-4

Number Theory Level 3

When $3^{1994}+2$ is divided by $11$ , the remainder is :

1 solution

Sai Venkatesh
Dec 22, 2014

${ 3 }^{ 5 }=243\equiv 1(mod\quad 11)$

Therefore $3^{ 1994 }=3^{ 4 }*3^{ 1990 }\equiv 81*1\equiv 4$ .

Therefore the remainder when $3^{1994}+2$ is divided by $11$ is $6$ .

I used FLT, but this is seriously cool!!

B.S.Bharath Sai Guhan - 6 years, 5 months ago

Alternate approaches are always welcome!

Krishna Ar - 6 years, 5 months ago