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HCF of 2^a - 1 and 2^b - 1 is 2^HCF(a,b) - 1

The same question, asked 2 times: CDS 1 2023*, CDS 2 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  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 2 2024

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

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