1967 AHSME Problems/Problem 31

Problem

Let $D=a^2+b^2+c^2$ , where $a$ , $b$ , are consecutive integers and $c=ab$ . Then $\sqrt{D}$ is:

$\textbf{(A)}\ \text{always an even integer}\qquad \textbf{(B)}\ \text{sometimes an odd integer, sometimes not}\\ \textbf{(C)}\ \text{always an odd integer}\qquad \textbf{(D)}\ \text{sometimes rational, sometimes not}\\ \textbf{(E)}\ \text{always irrational}$

Solution

$\fbox{C}$

1967 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 30	Followed by Problem 32
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1967 AHSME Problems/Problem 31

Problem

Solution

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