Find the remainder when 7^23 is divided by 25 Solution 7^23 = (7^22) . 7 = [ (7^2)^11] . 7 = [(50 - 1)^11] .7 Now In expansion of (50 - 1)^11 , all terms except the last one will be divisible by 25 since they contain an exponent of 50 in them. Last term = 11C11 * (-1) So we are left with (-1)(7) = -7 so 25 - 7 =18which is the remainder.