Question

Let p=2n+1 for n=10, 20, 30, or 40. For which value of n does p2−1 have the most factors?

Answer 1

For n= 40 p has 7 factors

For n= 20 p has 7 factors

For n= 10 p has 6 factors

For n= 30 p has 6 factors

Explanation:

p = 2n + 1

Putting the value of n= 10

p1= 20+1= 21

Putting the value of n= 20

p2= 40+1= 41

Putting the value of n= 30

p3= 60+1= 61

Putting the value of n= 40

p4= 80+1= 81

p2- 1= (p+1)(p-1)

= (81+1)(81-1)

=( 82)(80)

= 6560

= (1312)5

= 328)4)5

= 41 (2)(2)(2)(2)(2)(5)

p2- 1= (p+1)(p-1)

= (61+1)(61-1)

=( 62)(60)

=3720

= (465)(8)

= (93)(5)(8)

= (31)(3)(5)(2)(2)(2)

p2- 1= (p+1)(p-1)

= (41+1)(41-1)

=( 42)(40)

= 1680

= (7)(3)(5*2)(2*2*2)

p2- 1= (p+1)(p-1)

= (21+1)(21-1)

=( 22)(20)

= 440

= (11)(2)(5)(2)(2)