Question

x and y are natural numbers, and y≠1. It is known that (7x+1) is divisible by y and (8x+3) is also divisible by y. Find y.

Answer 1

Given : x and y are natural numbers . As (7x+1) is divisible by y and (8x+3) is also divisible by y.

To find: y

Solution: Since  (7 x+1) is divisible by y and (8 x+3) is also divisible by y.

1.As x,y are natural numbers, So

→8 x+3>7 x+1

→8 x+3=7 x+1+k y where k is any natural number.-------(1)[reason: 4 is divisible by 2 and 6 is also divisible by 2, so 6=4+2k]

→8 x-7 x+3-1=k y

→k y= x+2

If k=1, then y=x+2.

So value of y is x+2.As y≠1, so for different values of x there are different values of y. so x=1,we get y=3, as this is linear equation in one variable.

→y is an odd natural number,=[3,5,7,9,.....]≠1