Posted by **charlie** on Sunday, May 2, 2010 at 5:42pm.

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.

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.

## Answer this Question

## Related Questions

Math algebra - I'm reposting this, because Mathmate's answer hasn't directed me...

Math - Suppose you have two numbers. The difference of the two numbers is 12. ...

Math - When factoring a trinomial that is in the format Ax^2 + Bx + C, the ...

maths - the sum of N positive integers is 19. what is the maximum possible ...

Math - Two numbers have a product of 3 1/5 and a sum of 3 3/5. One of the ...

math - What is the lowest numberthat has a remainder of 1 when divided by 2 and ...

math 5th grade - two numbers have a product of 3 1/5 and a sum of 3 3/5. One of ...

Math - When they dial 3 and turn the oven on, it is like pushing the old button...

math - How do the ideas of divisibility and multiples relate to the study of ...

fifth frade fractions - Two numbers have a product of 3 1/5 and a sum of 3 3/5. ...