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.

- Nov 22nd 2010, 06:26 PMguidol92Sum of squares of digits dividing the number with those digits
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. - Nov 22nd 2010, 10:03 PMchiph588@
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. - Nov 22nd 2010, 10:03 PMchiph588@
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. - Nov 22nd 2010, 11:14 PMShanks
- Nov 23rd 2010, 03:40 PMchiph588@
- Nov 27th 2010, 02:38 PMqmech
A computer search finds the numbers: 1, 10, 20 and 50.

- Nov 28th 2010, 06:05 AMelemental
@Chip

$\displaystyle x^2 + y^2 | 10x + y$

so

$\displaystyle (x^2 + y^2)k = 10x + y$ - Nov 28th 2010, 09:22 PMchiph588@