How many numbers between 1 and 100 (excluded) satisfy that the sum of the squares of its digits divides the number?
Help please
Thank you.
Well clearly no one digit number greater than one satisfies this, so let's only look at two digit numbers.
Let $\displaystyle n=10x+y $ where $\displaystyle 0\leq x,y \leq 9 $
We need to solve the Diophantine Equation $\displaystyle x^2+y^2 = 10x+y $. Before I dive right in, let's see if you can do this.
Well clearly no one digit number greater than one satisfies this, so let's only look at two digit numbers.
Let $\displaystyle n=10x+y $ where $\displaystyle 0\leq x,y \leq 9 $
We need to solve the Diophantine Equation $\displaystyle \displaystyle x^2+y^2 = 10x+y $. Before I dive right in, let's see if you can do this.