question on remainder..

[silvia928]

If n is a positive integer, what is the remainder when (7^[4n+3])(6^n) is divided by 10?

Ans. 8

[ksh]

We can go ahead with considering n to be 1(+ve int)

then the stimulus= 7^7*3*2/10
Now units digit of 7^7=3
and 3*3*2=18/10 will leave us remainder as 8

thats the ans !

[netigen]

Silvia,

the way to solve these type of Qs is to realize that the power of 7 will have repeating unit digits for e.g.

unit digit of 7^1 = 7
unit digit of 7^2 = 9
unit digit of 7^3 = 3
unit digit of 7^4 = 1
unit digit of 7^5 = 7
unit digit of 7^6 = 9
unit digit of 7^7 = 3
unit digit of 7^8 = 1

We find that the unit digit repeats in cycles of 4

power of 7 is of the form 4n+3 which means that the unit digit will be 3

6^n will have unit digit = 6

so we get 6 x 3 = 8 in the units digit which will leave a remainder of 8

[wawatan]

great explanation, netigen!