Problema Solution
1. what is the remainder when 4 to the power 1000 is divided by 7??
2. for any integers a and b with HCF (a,b)=1, what is HCF ( a + b , a-b) equal to.. ??
Answer provided by our tutors
1.
4^1 has reminder 4
4^2 has reminder 2
4^3 has reminder 1
4^4 has reminder 4
....
we notice the following pattern
4^(3k + 1) has a reminder 4
4^(3k + 2) has a reminder 2
4^(3k) has a reminder 1
where k is integer, and k > 0
since 1000 = 3*333 + 1 and that is the 3k + 1 format we have
4^1000 divided by 7 has a reminder 4.