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The given mathematical expression is:

\[
20^{2004} + 16^{2004} - 3^{2004} - 1
\]

You are asked to find which of the given numbers divides the result of this expression. The options are:

1. 317
2. 323
3. 253
4. 91

To solve this, we will try to analyze the expression for divisibility by these numbers. One approach is to check for modular arithmetic properties or divisibility rules of each of these numbers.

Let me first compute for these numbers.The expression \(20^{2004} + 16^{2004} - 3^{2004} - 1\) is divisible by both 323 and 91. Thus, the correct options are:

- Option 2: 323
- Option 4: 91

Do you have any further questions or need more details? 

Here are 5 related questions:
1. How can you approach large exponent problems using modular arithmetic?
2. What are the properties of numbers like 323 and 91 that make them good divisors?
3. How can the Chinese remainder theorem help in solving such problems?
4. Can this method be applied to expressions with different exponents?
5. What are some advanced techniques for factoring large numbers?

**Tip:** When dealing with large powers in divisibility problems, modular arithmetic can simplify the calculations significantly.

20^2004 + 16^2004 - 3^2004 - 1, निम्न में से किसके द्वारा विभाज्य है?

Explore how to determine the divisibility of the expression 20^2004 + 16^2004 - 3^2004 - 1. This problem uses concepts of modular arithmetic and divisibility rules, suitable for high school students in Grades 10-12.

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