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.

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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.

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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.

Quote:

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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.

Quote:

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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.

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

Quote:

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Originally Posted by Shanks

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

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Pardon? (Thinking)

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

@Chip

so

Quote:

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Originally Posted by elemental

@Chip

so

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