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- - **Number of solutions**
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Number of solutionsFind the number of pairs $\displaystyle (n_1,n_2)$ that satisfies the equation below: $\displaystyle n_1 + n_2 = x\; \; $ where $\displaystyle n_1 ,n_2 ,x \in \mathbb{N}$ |

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$\displaystyle n_1 + n_2 = x$ $\displaystyle n_2 = x - n_1$ 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 |

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

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-Dan |

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

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-Dan |

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