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HCF of a^m - c and a^n - c: a^HCF(m,n) - 1 rule

This type of question, asked 2 times: CDS 1 2023, CDS 2 2024. All 3 questions below, oldest first.

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  1. Question 1

    CDS 1 2023

    1
    What is the largest number which divides both 235−12^{35}-1 and 291−12^{91}-1?

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  2. Question 2

    CDS 1 2023

    24
    What is the HCF of 329−93^{29} - 9 and 338−93^{38} - 9?

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  3. Question 3

    CDS 2 2024

    91
    What is the HCF of 236−12^{36} - 1 and 245−12^{45} - 1 ?

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