Question

Prove the divisibility of the following expressions:

Answer 1

Answer:

A divisibility test is a rule to determine whether one whole number is divisible by another number.

If after dividing a number by a number we get an integer then we can say that the number is divisible by the number.

1) Here, the given expression,

$\frac{10^6-5^7}{59}$

$=15625$

Which is an integer,

⇒ $10^6-5^7$ is divisible by 59.

2) Here, the given expression,

$\frac{81^7-27^9-9^{13}}{45}$

$=\frac{1.2709329142\times 10^{13}}{45}$

$=2.8242953648\times 10^{11}$

Which is an integer,

⇒ $81^7-27^9-9^{13}$ is divisible by 45.