If you add 168 to a certain number, it is exactly equal to the square of a positive integer. If you add 100, you can also get the square of another positive integer If you add 168 to a number, it is exactly equal to the square of a positive integer. If you add 100, you can also get the square of another positive integer. What is the number?

If you add 168 to a certain number, it is exactly equal to the square of a positive integer. If you add 100, you can also get the square of another positive integer If you add 168 to a number, it is exactly equal to the square of a positive integer. If you add 100, you can also get the square of another positive integer. What is the number?

Let this number be X,
attempt
x+100 = y^2
x+168 = (y+1)^2
unsolvable
Try again
x+100 = y^2
x+168 = (y+1)^2
We get x = 156
That is 156 + 100 = 256 = 16 ^ 2
156 + 168 = 324 = 18^2

Given that m and N are positive integers, and m ^ 2-N ^ 2 = 68, find m, n

m^2-n^2=68
(m+n)(m-n)=34*2
m+n=34
m-n=2
m=18
n=16