Question about Operations: Natural Numbers
Subject Mathematics
Mathematics
Source Insper
Insper
Topic Operations: Natural Numbers
Operations: Natural Numbers
Difficulty Medium
Medium
(Insper 2008) - Question Medium of Mathematics
One of the most famous problems in the history of mathematics, the 'Fermat's Last Theorem' was solved in 1995 by the Englishman Andrew Wiles. Demonstrating this theorem represented a great challenge to the brightest mathematicians for over 350 years, despite its statement being relatively simple, as shown below: If $$n$$ is a natural number greater than 2, then the equation $$x^{n}=y^{n}+z^{n}$$ does not have solutions where $$x, y$$, and $$z$$ are simultaneously positive integers. However, for $$n=2$$, the equation $$x^{n}=y^{n}+z^{n}$$ admits solutions under the conditions of the theorem stated above. One of these solutions is given bya.
$$x=1, y=0.6$$ and $$z=0.8$$.
b.
$$x=\sqrt{5}, y=1$$ and $$z=2$$.
c.
$$x=3, y=4$$ and $$z=5$$.
d.
$$x=1, y=1$$ and $$z=0$$.
e.
$$x=13, y=12$$ and $$z=5$$.
Answer sheet:
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