Posted by **charlie** on Monday, May 3, 2010 at 9:49am.

I'm reposting this, because Mathmate's answer hasn't directed me to the WHY? part of the question. Any prompts appreciated.

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.

Charlie

[math - MathMate, Sunday, May 2, 2010 at 5:49pm

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:

(7m+1)(7n+1)

Expand the product and complete the proof.]

The expansion seems to be:

49mn+7m+7n+1

I'm not seeing where's next in explaining WHY?

Thanks

Charlie

## Answer this Question

## Related Questions

- math - I have this question to work on, and I don't know where to start ...
- Math - When factoring a trinomial that is in the format Ax^2 + Bx + C, the ...
- Math - Suppose you have two numbers. The difference of the two numbers is 12. ...
- programming - 1. Write a structured algorithm that prompts the user to input two...
- Algebra - (5x^3-6x^2+8)/(x-4). (4) 5 -6 8 5 14 72 For the remainder I divided 72...
- statistics - this is to mathmate...this is jimmy and you answered by questions ...
- Math - Two numbers have a product of 3 1/5 and a sum of 3 3/5. One of the ...
- math 5th grade - two numbers have a product of 3 1/5 and a sum of 3 3/5. One of ...
- Math - The number 4641 can be expressed as the product of two 2-digit whole ...
- Math - The sum of two whole numbers is 9,and their positive difference is 5.what...

More Related Questions