Rational numbers

[Dr.Peterson]

Here is the whole problem. The part written bellow is the explanation I was given which I do not understand. Why does (90-5k)/12 have to be a whole number?
View attachment 32062

There has to be something still omitted.

This is not true, for example, if x is a perfect square.

What does the problem (or its context) tell you about x? Is it perhaps required to be prime, or a "square-free integer"?

In the other example you gave in #10 (which I assume is not the actual problem you are asking about), you have two primes, so what they say is true. It is not true in general.

If you won't follow instructions and show the entire problem, why should we try to help you?

 

[JeffM]

There has to be something still omitted.

This is not true, for example, if x is a perfect square.

What does the problem (or its context) tell you about x? Is it perhaps required to be prime, or a "square-free integer"?

In the other example you gave in #10 (which I assume is not the actual problem you are asking about), you have two primes, so what they say is true. It is not true in general.

If you won't follow instructions and show the entire problem, why should we try to help you?

I agree with your point. Notice that there is no x in the actual problem (assuming post # 10 is fairly close to a complete translation of the actual problem).

His last problem dealt with the binomial theorem. I suspect that, as I indicated in my previous post, that all that is necessary in this problem is to apply the binomial theorem to [imath](\sqrt[3]{3} + \sqrt{2})^5[/imath].

His problems are tricky enough that I think the moderators should suspend him if he fails again to give the complete and exact statement of the problem.

 

[Dr.Peterson]

Notice that there is no x in the actual problem (assuming post # 10 is fairly close to a complete translation of the actual problem).

But here is what he said for #4 and #10:

Here is the whole problem. The part written bellow is the explanation I was given which I do not understand. Why does (90-5k)/12 have to be a whole number?

Here is an example with actual numbers that I found which uses the same method.

I think it's been more or less clearly stated that the actual problem (by contrast) uses variables, and the example with numbers is provided only as an example of the thinking.

But, yes, the binomial theorem is the main idea; and if the actual, actual problem uses numbers, then everything becomes clearer.

 

[Loki123]

There has to be something still omitted.

This is not true, for example, if x is a perfect square.

What does the problem (or its context) tell you about x? Is it perhaps required to be prime, or a "square-free integer"?

In the other example you gave in #10 (which I assume is not the actual problem you are asking about), you have two primes, so what they say is true. It is not true in general.

If you won't follow instructions and show the entire problem, why should we try to help you?

I am sorry. I showed the entire problem when I asked. I was only confused about one part so that's why I at first posted only about that. I'll try to be more careful about that. As for if something is missing, I wrote this problem exactly as I was given and I even found a different problem with the same issues just to see if I was missing something or not. Sorry again I will try to inform you about everything from now on.