Q). If P =

, then the remainder when (P + 4) is divided by 13 is

Dear Student,

Please find below the solution to the asked query:

Given : P = m = 112m× m! , So

P = 1× 1!+2× 2!+3× 3!+4× 4!+ . . . +12× 12!P =  2 -1× 1!+ 3 -1× 2!+ 4 -1× 3!+ 3 -1× 4!+ . . . + 13 - 1× 12!P =   2! -1!+  3! -2!+  4! -3!+  5! -4!+ . . . +  13! -12!P =    2! -1!+   3! -2!+   4! -3!+   5! -4!+ . . . + 13! -12!P =13! -1!Then we divide ' p ' by 13 , So Remainder = P13 = 13! -1!13 = = 13! 13-1!13 = 0 - 1 =- 1
So,

Remainder when we divide P by 13  = -1 + 13 =  12 

But we have to divide P + 4  , So remainder when we divide  ' P + 4 ' by 13 :

Remainder = 12 + 4 =  16   =13 + 3  = 0 + 3 = 3

Therefore,

When we divide ' P + 4 ' by 13 we get remainder  = 3                                    ( Ans )


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