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Square (or even power) of an odd integer is of the form 8n + 1

This type of question, asked 5 times: CDS 2 2016, CDS 1 2017, CDS 1 2022, CDS 1 2023, CDS 1 2026. All 5 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    27
    Consider the following statements in respect of positive odd integers xx and yy : 1. x2+y2x^2 + y^2 is even integer. 2. x2+y2x^2 + y^2 is divisible by 4. Which of the above statements is/are correct ?

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  2. Question 2

    CDS 1 2017

    46
    Consider the following statements : 1. Of two consecutive integers, one is even. 2. Square of an odd integer is of the form 8n+18n + 1. Which of the above statements is/are correct ?

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  3. Question 3

    CDS 1 2022

    34
    Consider the following statements : 1. The sum of the cubes of three consecutive natural numbers is divisible by 9. 2. Every even power of every odd number (>1> 1) when divided by 8 gives 1 as remainder. Which of the above statements is/are correct?

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  4. Question 4

    CDS 1 2023

    15
    When every even power of every odd integer (greater than 1) is divided by 8, what is the remainder?

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  5. Question 5

    CDS 1 2026

    31
    Let P=N2P = N^2 where N is an odd integer. What is the remainder when P is divided by 8 ?

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