Thread: Sum 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.

Originally Posted by guidol92

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 where

We need to solve the Diophantine Equation . Before I dive right in, let's see if you can do this.

Originally Posted by guidol92

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 where

We need to solve the Diophantine Equation . Before I dive right in, let's see if you can do this.

Originally Posted by chiph588@

Well clearly no one digit number greater than one satisfies this, so let's only look at two digit numbers.

Let where

We need to solve the Diophantine Equation . Before I dive right in, let's see if you can do this.

Do you notice the word "divides", not "equal to" in x^2+y^2 = 10x+y.

Originally Posted by Shanks

Do you notice the word "divides", not "equal to" in x^2+y^2 = 10x+y.

Pardon?

A computer search finds the numbers: 1, 10, 20 and 50.

@Chip

so

Originally Posted by elemental

@Chip

so

Ohh, I read the question wrong as Shanks was pointing out.