If 7^(1983) is divided by 100, what is the remainder?
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
but how? could you explain it a bit more?
There are many ways we could solve this, I have used Binomial + Euler-Fermat's theorem.
very fancy math. here is how a bone head does it, in case it is not clear.
\[7^0=1,7^1=7,7^2=49,7^3=343,7^4=2401\] and once you see the "one" at the end of 2401, you know the pattern will repeat so that when you divide by 100 you only have 3 choices of remainders, 1,7,49,43 and they repeat in that order.
to figure out which one you have, divide 1883 by 4 and take the integer remainder, which is fairly clearly 3 because 4 divides 1880 evenly, leaving 3 as the remainder. so your choice is