# Number of solutions

#### idontknow

Find the number of pairs $$\displaystyle (n_1,n_2)$$ that satisfies the equation below:
$$\displaystyle n_1 + n_2 = x\; \;$$ where $$\displaystyle n_1 ,n_2 ,x \in \mathbb{N}$$

Last edited:

#### topsquark

Math Team
Find the number of pairs $$\displaystyle (n_1,n_2)$$ that satisfies the equation below:
$$\displaystyle n_1 + n_2 = x\; \;$$ where $$\displaystyle n_1 ,n_2 ,x \in \mathbb{N}$$
Let's rephrase the problem statement a bit.
$$\displaystyle n_1 + n_2 = x$$

$$\displaystyle n_2 = x - n_1$$

So
$$\displaystyle n_1 = 1$$, $$\displaystyle n_2 = x - 1$$.

$$\displaystyle n_1 = 2$$, $$\displaystyle n_2 = x - 2$$.

And now it's a counting problem. How many values can $$\displaystyle n_1$$ take on?

-Dan

#### idontknow

It is seen that $$\displaystyle x\geq 2$$
Number of pairs is dependent on $$\displaystyle x$$
Example , $$\displaystyle x=10^{10}$$

#### topsquark

Math Team
It is seen that $$\displaystyle x\geq 2$$
Number of pairs is dependent on $$\displaystyle x$$
Example , $$\displaystyle x=10^{10}$$
Yes. Though I'm not going to try to list all that with your x value!

-Dan

1 person

#### idontknow

What i got is $$\displaystyle f(x)=x-1$$
Where f(x) is the number of pairs

#### topsquark

Math Team
What i got is $$\displaystyle f(x)=x-1$$
Where f(x) is the number of pairs
Yes.

-Dan