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in Mathematics by (150k points)

The remainder left out when 82n – (62)2n +1 is divided by 9 is

(a) 2 

(b) 7

(c) 8 

(d) 0

1 Answer

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Best answer

(a) : Ist Solution : Using Modulo Arithmetic
8 = –1 (modulo 9) Also 62 = –1 (modulo 9)
⇒ 82n – (62)2n + 1 = [(–1)2n – (–1)2n + 1]mod 9
= (1 + 1)mod 9 = 2 mod 9 ⇒ Remainder = 2

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