Math algebra
posted by charlie .
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

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
Respond to this Question
Similar Questions

algebra
When dividing 2x2  4x + 5 by (x  1) the remainder is 11. True or false If you mean (2x^2  4x + 5)/(x1) , the quotient is (2x  2) with a remainder of 3. So False is the answer. 
Math
Suppose you have two numbers. The difference of the two numbers is 12. The product of the two numbers is 17. Multiply the larger of the two numbers by 100, add 50 times the smaller number to that, round the total to the nearest whole … 
Math
When factoring a trinomial that is in the format Ax^2 + Bx + C, the number that is represented by B should be viewed as the _____? 
Algebra
(5x^36x^2+8)/(x4). (4) 5 6 8 5 14 72 For the remainder I divided 72/4 for 18. So the whole answer would be 5x^3+14x^2+18. But the book's answer is 5x^2+14x56+232/(x4). Where did these numbers come from and where did I mess up? 
math
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. … 
Math
Two numbers have a product of 3 1/5 and a sum of 3 3/5. One of the numbers is a whole number. Find the numbers. 
statistics
this is to mathmate...this is jimmy and you answered by questions on random sample and probability (better business bureau question)..i greatly appreciate your help but i do not understand part b and d answers..i am totally lost on … 
programming
1. Write a structured algorithm that prompts the user to input two numbers. The algorithm should calculate and print the sum & product of the two numbers [21/2] 
Math
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other. 
mathematicsAlgebra
I think of two whole numbers;the product of the average of the sum and difference of the numbers and the difference of the sum and difference of the numbers is 12.if three times the first added to the second makes up 11..find the two …