Divisibility Rules

Step 1: Rewrite the given expression. Given expression:

2%5E%7B4n%7D%20-%2015n%20-%201

Since:

2%5E%7B4n%7D%20%3D%20(2%5E4)%5En%20%3D%2016%5En

the expression becomes:

16%5En%20-%2015n%20-%201

Step 2: Check with small values of $n$ . For

n%20%3D%201

16%5E1%20-%2015(1)%20-%201%20%3D%2016%20-%2015%20-%201%20%3D%200%0A%5Cquad%20%5Ctext%7B(divisible%20by%20any%20number)%7D

For

n%20%3D%202

16%5E2%20-%2015(2)%20-%201%20%3D%20256%20-%2030%20-%201%20%3D%20225

and

225%20%5Cdiv%20225%20%3D%201%0A%5Cquad%20%5Ctext%7B(exact%20division)%7D

For

n%20%3D%203

16%5E3%20-%2015(3)%20-%201%20%3D%204096%20-%2045%20-%201%20%3D%204050

and

4050%20%5Cdiv%20225%20%3D%2018%0A%5Cquad%20%5Ctext%7B(exact%20division)%7D

Thus, the expression is divisible by

225

for multiple values of

n

.
Step 3: Conclude the answer. Therefore,

2%5E%7B4n%7D%20-%2015n%20-%201

is divisible by

225

Chapter Questions
1 MCQs