What is the remainder when 1273^4 + 1273^2 - 1273^5 is divided by 24.Please explain me the procedure also..?

Answer 1

The value 1273 = 1 mod 24
now (1273)^4 mod 24 = (1)^4 = 1
now (1273)^2 mod 24 = (1)^2 = 1
now (1273)^5 mod 24 = (1)^5 =1

The above is because a^n mod m = (a mod m)^n mod m
we chose -1 inplace of 23 for simplicity
so the sum mod 24 = 1+1 - 1= 3
So remaineder is 1 mod 24 = 1

The above is true becuase (a + b) mod m = (a mod m + b mod m) mod m

(The person below mentioned that I fumbled on sign and based on that I have don the corrections, Thanks to him.)

Answer 2

1273^4 + 1273^2 - 1273^5
=1273^(4+2-5)
=1273^(1)
=1273
1273^4 + 1273^2 - 1273^5 is divided by 24.
=1273/24
=53 1/24

so, the remainder is 1 with 53 as a quotient and 24 as a divisor.

Answer 3

1273^4 + 1273^2-1273^5=1273^1.6
it is 1273^1.6 since all the numbers ie 1273 are the same it makes it possible to use the laws of indices i.e. when you add two powers you actually multiply them and when you minus two powers you actually divide them so if you add 1273^4+1273^2 you get 1273^8 and then divide this by 1273^5 which gives you 1273^1.6.

1273^1.6=92837.92944 and divide this by 24 and you are left with 3868.24706.

Answer 4

Ooops..... math_kp fumbled the sign ☺
1273/24 = 53 R1 so each of the terms reduces to 1(mod 24) and the total is 1^4 + 1^2 - 1^5 = 1


Doug