# Math algebra

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

1. 👍
2. 👎
3. 👁
1. you are looking at it ...

49mn+7m+7n+1
= 7(mn+m+n) +1

isn't mn+m+n an integer?

so the last expression has the form of 7k+1 which would leave a remainder of 1 when divided by 7

1. 👍
2. 👎

## Similar Questions

1. ### Chemistry

Part A Calculate the standard enthalpy change for the reaction 2A+B --->2C +2D Use the following data: Substance Delta H(kJ/mol) A -263 B -391 C +203 D -523 Express your answer in kilojoules. MY ANSWER FOR PART A: Delta H =277 kJ

2. ### FINANCE

You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 35-year mortgage loan for 75 percent of the \$3,250,000 purchase price. The monthly payment on this loan will be \$15,800. Requirement 1: What

3. ### Trigonometry

The area of a square garden is 300 m^2. How long is the diagonal? a. 5√6 m b. 150 m c.10√6 m d. 900 m Hello! I'd appreciate any help I could get on this! I don't understand it very well and every equation that I know and tried

4. ### Math (Physics)

Problem: An excited hydrogen atom could, in principle, have a radius of 2.50 mm . ________ Part A: What would be the value of n for a Bohr orbit of this size? Answer--> n= 6.87×103 _______ Part B What would its energy be?

A 0.130kg baseball pitched at 35.5 m/s is hit on a horizontal line drive straight back at the pitcher at 50.5 m/s . Part a: If the contact time between bat and ball is 4.25×10^−3 , calculate the magnitude of the force (assumed

2. ### geometry

Find point Z that partitions the directed line segment XY in the ratio of 5:3 where X(-2, 6) and Y(-10, -2). Its by using the part to part method

3. ### english

Choose the word needing an apostrophe or an apostrophe and an s. If the sentences is correct, choose no error. 1. Why havent you dotted your j’s? haven’t **** j’s’ no error 2. Ounce for ounce, humans aren’t as strong as

4. ### chemistry

Write a balanced equation for the neutralization of each of the following. Express your answer as a chemical equation. Identify all of the phases in your answer. Part A: H3PO4(aq) and NaOH(aq) Part B: Hl(aq) and LiOH(aq) Part C:

1. ### math:)

Vector u is represented by the directed line segment RS and vector v is represented by the directed line segment OP. If R=(8,-2), S=(11,-6), O=(-3,-9), and P=(0,-13), are u and v equal? Explain how you reached your answer.

2. ### physics

A jet plane is flying with a constant speed along a straight line, at an angle of 30.0° above the horizontal, as shown in part (a) of the drawing. The plane has a weight of magnitude 87500 N, and its engines provide a forward

3. ### PHYSICS

On vacation, your 1400-kg car pulls a 520-kg trailer away from a stoplight with an acceleration of 2.00 m/s2 . A: What is the net force exerted by the car on the trailer? Assume that the positive x axis is directed toward the

4. ### physics

Three forces act on a moving object. One force has a magnitude of 61.9 N and is directed due north. Another has a magnitude of 52.0 N and is directed due west. What must be (a) the magnitude and (b) the direction of the third