Question

If N = 82pow3 - 62pow3 -
20pow3 then N is divisible by:
a) 31 and 41
b) 13 and 67
c) 17 and 7
d) none

Answer 1

Answer:

31 and 41

Step-by-step explanation:

N = 82^3 - 62^3 -20^3

N = 2^3 ( 41^3 - 31^3 - 10^3 )  

N = 8 [ ( 41-31 ) ( 41^2 + 31^2 + 41*31 ) - 10^3 ]    

                                                           [ ∵  a^3 - b^3 = (a-b)*{(a)^2 + (b)^2 + a*b)]

N = 80 ( 1681 + 961 + 1271 - 100 )

N = 80 ( 3813 )

N = 80 ( 41 ) ( 93 )

N = 80 "(41) (31)" 3

∴ N is divisible by both 41 and 31.