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I have this question to work on, and I don't know where to start investigating the answer:

The product of any two (whole) numbers each of which leave a remainder of 1 on dividing by 7, also leaves a remainder of 1 on dividing by 7. Why?

I THINK that I can see a quadratic in there ( (n+1)(2n+1) ); and when I multiply any variation out, there's always a remainder 1.

Can anyone confirm the link; and point me where to go next? Could i use a diagram to explain it? Thanks.


  • math -

    An integer that leaves a remainder of 1 when divided by 7 can be represented by
    7m+1, or 7n+1, where m, n are integers.

    The product is thus:

    Expand the product and complete the proof.

  • math -

    you will have to exolain it by yourself😿💦💦💦💦

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