Find the least residue of 7^5 mod 50 without using a calculator.
so far i have 7=7 mod 50 7^5 = 7^5 mod 50 7^2 = 49 7^3=343 since 7^2=(-1)mod50 and 7^3=(-43)mod50 it follows that 7^6=7^2 * 7^3 = (-) = 43 feel like this is wrong though could somebody explain where i have made an error?