<P><A name="[문서의 처음]"></A></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">수학적 귀납법을 사용하여, (a,b)=1 이면 모든 n≥1에 대하여 (a,bⁿ)=1 임을 증명하라. </SPAN></P><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '한컴바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '한컴바탕'; TEXT-ALIGN: justify"><BR>라는 문제에 대한 답변으로 </P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '한컴바탕'; TEXT-ALIGN: justify"> </P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '한컴바탕'; TEXT-ALIGN: justify"><A name="[문서의 처음]"></A></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">굳이 수학적 귀납법을 사용한다면, 아래 정도로 표현이 됩니다. </SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"><BR></SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">n=1일 때, (a,b)=1이면, (a,b^1)=1은 성립한다.</SPAN><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"></SPAN> </P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"><BR></SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">n=k일 때, 성립한다고 가정한다. 즉, (a,b)=1이면, (a,b^k)=1이다.</SPAN><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"></SPAN> </P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"><BR></SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">n=k+1일 때, (a,b)=1이면, (a,b^k+1)=1 이다. </SPAN><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"></SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"><BR></SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"> 왜냐하면, ① (a,b)=1이고, (∵ 조건)</SPAN><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"></SPAN> </P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"><BR></SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"> ② (a,b^k)=1 ( ∵ n=k일 때, 가정) 이므로, </SPAN><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"></SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"><BR></SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"> (a,bxb^k)=1이다. 즉 (a,b^k+1)=1 이다. </SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"></SPAN> </P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">라고 해주셨는데</SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"><A name="[문서의 처음]"></A> </P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">(a, b^k)=1 즉, au+b^kv=1 (b^kv=1-au) 을 이용해서 </SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">(a, b^k+1)=1이 되는 걸 증명할 순 없을까요?</SPAN></P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify">그리고 위의 부분에서 <SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">①, ②</SPAN> 번을 통해 결론이 나오는 부분</P> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '바탕'; TEXT-ALIGN: justify">증명을 모르겠어요..</P></SPAN> <P style="FONT-SIZE: 10pt; MARGIN: 0px; COLOR: #000000; TEXT-INDENT: 0px; LINE-HEIGHT: 160%; FONT-FAMILY: '한컴바탕'; TEXT-ALIGN: justify"><SPAN style="FONT-SIZE: 10pt; COLOR: #000000; LINE-HEIGHT: 21px; FONT-FAMILY: '한컴바탕'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"><BR></SPAN></P></SPAN>
