76n - 66n, where n is an integer > 0, is divisible by :
A. 13
B. 127
C. 559
D. All the above
Answer: Option D
Solution(By Examveda Team)
When n is even, (xn - an) is divisible by both (x - a) as well as (x + a).Now,
(76n - 66n)
= [(73)2n - (63)2n]
= [(343)2n - (216)2n]
∴ (76n - 66n) is divisible by both (7 - 6) and (7 + 6)
(76n - 66n) is divisible by 13
And, [(343)2n - (216)2n] is divisible by both (343 - 216) and (343 + 216)
⇒ (76n - 66n) is divisible by both 127 and 559
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
Join The Discussion