Simple and Basic

Never heard of the Fermat Theorem......

@ jeetopper : Can u post the solution ?

@ abhisek
is not 2^1/1 leaves remainder zero??
ur observation only holds if the power of 2 is prime..
and actually this is fermat theorem. which says a ^p = a mod p where p is prime..

A = b mod c means A-b can be divided by c or A leaves remainder b ,when divided by C( if and only if C> b).
example : 64 = 1 mod 3 also 64 = 4 mod 3,(but 1 is the remainder not 4)

Now coming to the question, in order to apply fermat theorem we have to pray that 1991 is prime.
as 1991 is not prime ,i think fermat theorem can not be applied here///

there is another theorem of fermat which says (A+B)^ P =( A^p + B^p) mod p,again p is prime.....

Yes i agree , the 1st statement (remainder of 2¹/1 = 2) is incorrect....and i got the Fermat's Theorem....

remainder is 559