Prove that the square of an odd number is always 1 more than a multiple of 4

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Prove that the square of an odd number is always 1 more than a multiple of 4

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Gia Bảo 6 months 2021-07-25T20:54:32+00:00 1 Answers 16 views 0

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    2021-07-25T20:56:05+00:00

    Answer:

    By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.

    Step-by-step explanation:

    For examples,

    Let’s consider squares of 3, 11, 25, 37 and 131.

     {3}^{2}  = 9

    8 is a multiple of 4, and 9 is more than 8.

     {11}^{2}  = 121

    120 is a multiple of 4 and 121 is one more than it.

     {25}^{2}  = 625

    624 is a multiple of 4 and 625 is one more than it.

     {37}^{2}  = 1369

    1368 is a multiple of 4 and 1369 is one more than 1368.

     {131}^{2}  = 17161

    17160 is a multiple of 4.

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