Prove algebraically that the square of any number is always 1 more than a multiple of 8

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Prove algebraically that the square of any number is always 1 more than a multiple of 8

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Thái Dương 3 years 2021-08-24T22:34:37+00:00 1 Answers 41 views 0

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  1. MichaelMet
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    2021-08-24T22:35:41+00:00
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    Answer:

    This is interesting but I don’t think it’s provable (unless it’s just the square of odd numbers).

    3² = 9, which is 1 more than a multiple of 8  (8)

    4² = 16, which is not 1 more than a multiple of 8  (8)

    5² = 25, which is 1 more than a multiple of 8  (24)

    6² = 36, which is not 1 more than a multiple of 8  (32)

    7² = 49, which is 1 more than a multiple of 8  (48)

    8² = 64, which is not 1 more than a multiple of 8  (64)

    9² = 81, which is 1 more than a multiple of 8  (80)

    10² = 100, which is not 1 more than a multiple of 8  (96)

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