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Algebraic expression in consecutive integers is a perfect square

This type of question, asked 2 times: CDS 2 2020, CDS 2 2024. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2020

    5
    If I=a2+b2+c2I = a^2 + b^2 + c^2, where aa and bb are consecutive integers and c=abc = ab, then II is

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  2. Question 2

    CDS 2 2024

    79
    Consider the following statements in respect of p=n(n+1)(n+2)(n+3)+1p = n(n+1)(n+2)(n+3) + 1, where nn is a natural number : I. pp is always odd II. pp is a perfect square Which of the statements given above is/are correct ?

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