Question

7^10 -5^10 divisible by

Answer 1

concepts : we know, x² - y² = (x - y)(x + y) , here we can say x² - y² is divisible by (x - y) and (x + y).
similarly, x³ - y³ = (x - y)(x² + y² + xy) , here x³ - y³ is divisible by (x - y)

similarly, x⁴ - y⁴ = (x - y)(x + y)(x² + y)², is too divisible by (x - y)

we get, xⁿ - yⁿ always divisible by (x - y). no matter what is the value of n , it is applicable even as well as odd value of n.

now, come to the question,

here it is given that, 7^10 - 5^10
if we assume 10 = n , x = 7 and y = 5 then, 7^10 - 5^10 converts into xⁿ - yⁿ.
so, this is similar case as I mentioned above .

hence, 7^10 - 5^10 always divisible by (7 - 5) = 2

Answer 2

Step-by-step explanation:

7¹⁰-5¹⁰=(7⁵)²-(5⁵)²

=(7⁵+5⁵)(7⁵-5⁵) (a²-b²=(a+b)(a-b)

(16807+3125)(7⁵-5⁵)

=19932(7⁵-5⁵)

now,19832 is divisible by 11

therefore 7¹⁰-5¹⁰ is divisible by 11.