Remainder-2

What is the remainder when 2 87 + 3 2^{87}+3 is divided by 7?


The answer is 4.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

2 λ ( 7 ) 2 6 1 ( m o d 7 ) 87 ( m o d 7 ) 87 7 × 12 + 3 3 ( m o d 7 ) 2 87 2 3 1 ( m o d 7 ) 2 87 + 3 4 ( m o d 7 ) \begin{aligned} 2^{\lambda(7)}\equiv 2^6\equiv 1&\pmod {7}\\ \implies\boxed{ 87\pmod{7}}\\ 87\equiv 7\times 12+3\equiv 3&\pmod{7}\\ \implies 2^{87}\equiv 2^3\equiv 1&\pmod{7}\\ \implies 2^{87}+3\equiv \boxed{4}&\pmod{7} \end{aligned}

good solution!...+1

Ayush G Rai - 5 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...