If x47  + 1 is divided by x2 - 1 what is the remainder? Pls show the working

Asked by Gurinder | 5th Dec, 2015, 09:03: PM

Expert Answer:

L e t space f open parentheses x close parentheses equals x to the power of 47 plus 1 g open parentheses x close parentheses equals x squared minus 1 equals open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses T h u s comma space w h e n space w e space d i v i d e space f open parentheses x close parentheses space b y space g open parentheses x close parentheses comma space w e space h a v e comma P open parentheses x close parentheses equals fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals fraction numerator x to the power of 47 plus 1 over denominator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses end fraction W e space k n o w space t h a t comma space x to the power of n plus 1 space i s space d i v i s i b l e space b y space x plus 1 space i f space n space i s space o d d. A n d space sin c e space 47 space i s space o d d comma space w e space h a v e comma space x to the power of 47 plus 1 space i s space d i v i s i b l e space b y space x plus 1. T h u s comma space w e space n e e d space t o space f i n d space t h e space r e m a i n d e r space w h e n space f open parentheses x close parentheses space i s space d i v i d e d space b y space x minus 1. T h e r e f o r e comma space t h e space r e m a i n d e r space i s space f open parentheses 1 close parentheses equals 1 to the power of 47 plus 1 equals 2

Answered by Vimala Ramamurthy | 7th Dec, 2015, 09:20: AM