confusion

[sujoy]

respected sir ,
Here is the problem that I could not solve:
It is given(17k-2)/13 gives "0" remainder. A student does not know the
table of 17,but he needs to get the value of "k".He is intelligent enough
to find a simplified expression governing "k" which gives the same value
of "k" as the expression written. Find what expression did he find?

answer-- (4k-2)/13

with regards& respect
Sujoy

 

[soroban]

Hello, sujoy!

It is given(17k-2)/13 gives "0" remainder.
A student does not know the table of 17, but he needs to get the value of "k".
He is intelligent enough to find a simplified expression governing "k"
which gives the same value of "k" as the expression written.
What expression did he find?

Answer: (4k-2)/13

I assume your question is: <u>How</u> did he find it?

He used "division" . . . it looks like this:

. . . 17k - 2 . . . .13k + 4k - 2 . . . .13k . .4k - 2 . . . . . . . 4k - 2
. . . --------- . = . --------------- . = . ---- + -------- . = . k + -------
. . . . .13 . . . . . . . . . 13 . . . . . . . . 13 . . . 13 . . . . . . . . . .13

To get a remainder of 0, he needs only the table-of-4.

And he will find that k = 7 gives the least (positive) solution.

In general: . k .= .7 + 13n .for any integer n.

 

[sujoy]

Respected Sir
Probably this is the best form of help a person can get. Your explanation has been so lucid & so clear, that I really liked it.
WITH A LOT OF RESPECT
THANK YOU VERY MUCH SIR& THANKS A LOT
REGARDS
Sujoy