Question

What is the remainder when 3 ^57 +27 is divided by 28?

Answer 1

(3)^ 3*19 + (28-1)

= 27 ^ 19 + (28-1)
= (28-1)^19 + (28-1)  

divide it by 28
 
remainder will be  -1/28 + (-1/28)  = -2/28  or 26 will be the remainder

hope it helped

Answer 2

Answer is 26. the remainder is 26 after dividing the expression by 28.

Step-by-step explanation:

We know that,

                                    ⇒ $3^{57} + 27$ divided by 28

Now, change the expression into usable form.

                                   ⇒ $(3^{3} )^{19} + 28 - 1$ = $(28 - 1)^{19} + 28 - 1$

                           

Now, breaking the above expression with power into descrete forms ( different component with plus sign after one component to another).

Now,

                                    =  $28^{19} + (-1)^{19} ............. + 28 - 1$

Every term of above equation has a multiple of 28 except $-1^{19}$ and -1.

So, according to that condition only these two terms are undividable by 28.

So, their solution

                                   ⇒ $\frac{-1^{19}}{28}$ - $\frac{1}{28}$ = $\frac{-2}{28}$

No. 2 is in negetive. It means from the divisable term, 2 must be sbtracted. So, subtracting 2 from 28, the answer will be 26.

                                     ⇒ 28 - 2 = 26