EIV 4th Ed. Ch. 10 problem set Question 9 -- please help

[futjim]

If mn = 3(m+1) + n and m and n are integers, m could be any of the following values EXCEPT:

- 2
- 3
- 4
- 5

The explanation at the back offered two approaches. I understand the first one but don't understand the second:

...you can notice that consecutive values of 5c + 8d differ by 3. In other words, every possible value of 5c + 8d equals a multiple of 3 plus some constant...

Question one: what is the rule here? What happens when a Multiple of 5, MO5, is added to a Multiple of 8, MO8? (I tried looking in the number properties book and found nothing)

I've also tried working this relationship out with numbers and found that if c & d in the above equation is different then the resulting number isn't a MO3. However, if c=d then the result is MO3 + some constant.

Please clarify the above relationship!!

Thanks alot!

[adiagr]

If mn = 3(m+1) + n and m and n are integers, m could be any of the following values EXCEPT:

- 2
- 3
- 4
- 5

The explanation at the back offered two approaches. I understand the first one but don't understand the second:

...you can notice that consecutive values of 5c + 8d differ by 3. In other words, every possible value of 5c + 8d equals a multiple of 3 plus some constant...

Question one: what is the rule here? What happens when a Multiple of 5, MO5, is added to a Multiple of 8, MO8? (I tried looking in the number properties book and found nothing)

I've also tried working this relationship out with numbers and found that if c & d in the above equation is different then the resulting number isn't a MO3. However, if c=d then the result is MO3 + some constant.

Please clarify the above relationship!!

Thanks alot!

separate out m and n.

mn-n = 3m +3

n*(m-1) = 3 *(m+1)

n = 3 * [(m+1) /(m-1)]

n is an integer.

it can be seen that n is integer for all given values of m except 5.

Aditya

[futjim]

Aditya, thank you so much for the reply.

I just realized the typed in the wrong question.

I'll repost it again.

Cheers,

[tim]

i don't know if you ever posted a corrected version of your problem, but please do when you get a chance, ALONG WITH a reference. The solution you mention looks really fishy and i don't think you typed it correctly..