Mathematical proof

[Pepe Le Mokko]

I know the solution provided is correct, but I am unable to prove it mathematically. Does anyone have an idea or a link to a full-proof demonstration ? Many thanks

http://www.excelforum.com/excel-gene...ml#post3811796

[xladept]

Hi Pepe,

These guys use a digit sum chart and(it appears, induction)?

[zbor]

Numerals whose sum of digits is divisible by 9 represent numbers divisible by 9!

The whole number is divisible by 9 if and only if the sum of the digits is.

This test may be applied recursively.

Any number you can present as n*9+k here 9 is greatest character of base 10. (k=0,1,2,3...,9 and n € Z (n = Integer))
If you take 28 = 3*9+1 then k=1 because 2+8 = 10 is not divisible by 9.
As you can repeat this recursively 1+0 will return 1.

At the end you will get k as with formula you provide.

For details go find more about divisibility by 9.

[Pepe Le Mokko]

Numerals whose sum of digits is divisible by 9 represent numbers divisible by 9!

The whole number is divisible by 9 if and only if the sum of the digits is.

This test may be applied recursively.

Any number you can present as n*9+k here 9 is greatest character of base 10. (k=0,1,2,3...,9 and n € Z (n = Integer))
If you take 28 = 3*9+1 then k=1 because 2+8 = 10 is not divisible by 9.
As you can repeat this recursively 1+0 will return 1.

At the end you will get k as with formula you provide.

For details go find more about divisibility by 9.

The divisibility by 9 is well known thank you.
This does not prove that mod9 returns the sum of each digit

[Pepe Le Mokko]

Hi Pepe,

These guys use a digit sum chart and(it appears, induction)?

Thank you

I had a look but could not find a proof

[ragulduy]

http://www.math.uiuc.edu/~hildebr/pu...rgrad10sol.pdf

Number 2 is what you are talking about I believe.

[Pepe Le Mokko]

That is it, thank you so much I am not very familiar with modular arithmetic, I'll brush up on it

[xladept]

I almost had it - I was on a similar track and had shown that the modulo 9 was tantamount to the sum of the digits and was trying to use the reductio