Question
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
= (-1)(-43)
= 43
feel like this is wrong though could somebody please explain where I have made an error?
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
= (-1)(-43)
= 43
feel like this is wrong though could somebody please explain where I have made an error?