Aptitude - Numbers - Discussion

Natural Numbers are 1,2,3,4,........... so on;

(i) when n = 1 , (xⁿ - aⁿ) = (x - a) which is divisible by (x - a).
(ii) when n = 2, (xⁿ - aⁿ) = x² - a² = (x - a)(x + a) which is divisible by (x-a).
(iii) when n = 3, (xⁿ - aⁿ) = x³ - a³ = (x-a)(x²+ax+a²) which is divisible by (x-a).

Here other numbers like 4 6 8 can be solved similarly like the (ii).
And other numbers like 5 7 8 can be solved similarly like the (iii).

which numbers are natural number? Please explain.

can someone explain it ?

@Suman: In a collection (or set) of objects (or elements), the act of determining the number of objects present is called counting. The numbers thus obtained are called the counting numbers or natural numbers (1, 2, 3, ). For an empty set, no object is present, and the count yields the number 0, which, appended to the natural numbers, produces what are known as the whole numbers.

@Navneet

Recall the formula (a^2 - b^2) here n is 2 which is even, this equation is equal to (a+b)(a-b) hence we can see it is divisible by (a+b) and (a-b).

Natural Numbers are 1,2,3,4,........... so on
(i) when n = 1 , (xⁿ - aⁿ) = (x - a) which is divisible by (x - a)
(ii) when n = 2, (xⁿ - aⁿ) = x² - a² = (x - a)(x + a) which is divisible by (x-a)
(iii) when n = 3, (xⁿ - aⁿ) = x³ - a³ = (x-a)(x²+ax+a²) which is divisible by (x-a)
other numbers like 4 6 8 can be solved similarly like the (ii)
other number like 5 7 8 can be solved similarly like the (iii)