Principle Of Mathematical Induction

Step 1: Define the function

Step 2: Try small values

, not divisible by 5 or 3

Step 3: General form and induction for divisibility by 7

Assume is divisible by 7

Then:

Substitute:

⟹ divisible by 7

Conclusion: There exists a prime integer (7) which divides for all .

Correct answer: There exists a prime integer which divides