Can Binomial theorem be helpful?

Number Theory Level 2

$Find\quad the\quad remainder\quad when\quad { 2 }^{ 55 }+1\quad is\quad divided\quad by\quad 11.$

The answer is 0.

1 solution

Achal Jain
Oct 5, 2015

We can write it as 32^11 + 1^11 Now according to Fermat Theorem if a and b are 2 integers with power p which is a prime it can be written as (a + b)^p. Hence we would get (33)^11 But 33 is divisible by 11 hence answer is 0

Can Binomial theorem be helpful?

The answer is 0.

1 solution

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