Question

which is not the factor of 4^6n-6^4n for any positive integer n
a.5
b.25
c.7
d. none

Answer 1

Given : 4⁶ⁿ - 6⁴ⁿ

To Find : which is not the factor of   for any positive integer n

a.5

b.25

c.7

d. none

Solution:

4⁶ⁿ - 6⁴ⁿ

put n = 1

=  4⁶ - 6⁴

= 4,096 - 1296

= 2,800

2800 = 2 x 2 x  2 x  2 x 5  x  5 x 7

Hence its divisible by 5

5 x 5 = 25

and 7

so 5 , 7 and 25 are the factors

None is the  correct answer

Another way :

4⁶ⁿ - 6⁴ⁿ

= 2¹²ⁿ - 2⁴ⁿ3⁴ⁿ

=  2⁴ⁿ(2⁸ⁿ - 3⁴ⁿ)

=  2⁴ⁿ(4⁴ⁿ - 3⁴ⁿ)

= 2⁴ⁿ(4²ⁿ + 3²ⁿ)(4²ⁿ - 3²ⁿ)

= 2⁴ⁿ(4²ⁿ + 3²ⁿ)(4ⁿ + 3ⁿ)(4ⁿ - 3ⁿ)

just putting n = 1

= 2⁴(16 + 9)(4  + 3 )(4  - 3 )

= 16 (25) (7) (1)

Hence  5, 7 & 25 are factors

Learn More:

Which statement about –2h2 – 15h – 7 is true? One of the factors is ...

https://brainly.in/question/9851118

Show that m-1 is a factor of m²¹-1 and m²²-1. - Brainly.in

https://brainly.in/question/4561423