SOLUTION: if N is divided by 7 the remainder is 4 and if same number N is divided by 8 the remainder is 2. what is the value of N?

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Question 770086: if N is divided by 7 the remainder is 4 and if same number N is divided by 8 the remainder is 2. what is the value of N?
Found 2 solutions by ramkikk66, KMST:
Answer by ramkikk66(644)   (Show Source): You can put this solution on YOUR website!
if N is divided by 7 the remainder is 4 and if same number N is divided by 8 the remainder is 2. what is the value of N?
Ans:
N divided by 7 gives remainder 4. So N can be written as 7*m + 4 for some integer m.
N divided by 8 gives remainder 2. So N can be written as 8*n + 2 for some integer n.
Equating the 2 expressions for N
7*m + 4 = 8*n + 2
7*m + 2 = 8*n
Need to find which integer values of m and n satisfy the above equation. Since it
is only 1 equation with 2 unknown variables m and n, we can do it only by trial
and error. Try different values for m (1,2,3..) and see if we get an integer 
value for n.
We see that one possible solution is m = 2, n = 2
7*2 + 2 = 8*2
So the number N is 7*m + 4 = 18.
Check: 18 div by 7 gives remainder 4, 18 div by 8 gives remainder 2 :)
There are other solutions too - e.g. 74 also gives 4 as remainder when divided
by 7 and a remainder of 2 when divided by 8. But 18 is the smallest such number.
:)


Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
From you get
-->-->-->
would yield a negative ,
and a negative ,
and that does not make sense.
could be 0, 1, 2, 3, ...
For we get -->-->-->
But there is an infinite number of other solutions.
yields -->-->-->
yields -->-->-->
and so on.
After finding as one solution, we can keep getting more solutions by adding each time.
Since has a remainder of when divided by either or , adding or a multiple of does not change the remainders.
In general, we could rename as and say that is a non-negative integer.
Then and -->-->
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