主辦單位 文安

關於AMC高級組第八題題目

珍妮的年齡是一個質數,安迪的年齡比珍妮大一歲,
且他的年齡有8個因數,下列哪一個數可能為他們的
年齡和?(A)27(B)39(C)75(D)87(E)107

若解答無誤
則題目應改為正因數個數有8個

若題目無誤
則答案應改為A,C

攸關考生權利,請查察

謝謝~~

江老師以及學生湯曉薇 謹上 2007.11.5

該題英文原文是：

8. Jane’s age is a prime number. Andy’s age has 8 factors and he is one year older
than Jane. Of the following numbers, which could be the sum of their ages?
(A) 27 (B) 39 (C) 75 (D) 87 (E) 107


我個人認為在一般數論中，如無特別聲明，因數及質數都是指正數。我將會把您的意見反應給澳洲主辦單位。

_________________
孫文先 敬上

澳洲的回應：

Dear Wen-Hsien

In this context, in English, we would always assume the factors are positive. We find that it can be impossible if you have to counter this, at the next level they could say it is more if the factors can be complex. To cover this we would sometimes need so many words we distract from the real point of the question. So in English we have no difficulty, that people would assume the factors are positive if not otherwise made clear.

_________________
孫文先 敬上

　　這的確是個困擾，如同解一元二次方程式，若無特別指定，則複數算為無解．
　　若因數要特別說明是正因數，也實在累人．另外，多項式的因式，加上任何係數都算是因式一種，也會變成無限多種．

謝謝~~~