Question

find the remainder when 59^28 is divided by 7

Answer 1

You need to look for a pattern here

Answer 2

So check a few exponents and see if you can see a pattern

Answer 3

(7*8+3)^28

Answer 4

Yes, this requires binomial theorem, do you know how it works?

Answer 5

i am relying on the formula(ax+1)^n/a which gives remainder as 1

Answer 6

you know the cycle of 8 how it goes right?---------->8,4,2,6 and it repeats. mow 58 means take unit digit 8 from that and then raise to power 6 which gives remainder 8. divide remainder by 7------->1 is the remainder

Answer 7

the book is showing the remainder as 4

Answer 8

Yeah 4 is the remainder

Answer 9

whats the trick to find remainder of 2^14/7

Answer 10

yeah got it unit digit is 6 as we can see the process....now counting 6 times from tops give you 4 and dividing 4/7= 4 as remainder

Answer 11

see it as 8^6-------> 4 as unit digit.