코딩 연습

Find the smallest \(x+y+z\) with integers \(x>y>z>0\) such that \(x+y\), \(x-y\), \(x+z\), \(x-z\), \(y+z\), \(y-z\) are all perfect squares. \(x>y>z>0\) 을 만족하는 자연수 \(x, \; y\; z\) 에 대해서 \(x+y\), \(x-y\), \(x+z\), \(x-z\), \(y+z\), \(y-z\) 가 모두 완전제곱수가 되는 \(x+y+z\) 의 최솟값을 구하시오. 늘 그렇듯이 처음엔 무식하게 하나하나 완전제곱수인 것을 모두 확인하는 방법을 사용했지만, 아니나 다를까 시간이 너무 오래 걸린다. 그래서 다음의 방법을 생각 !! \[x+y=a^2 \label{a}\tag{1}\] ..

A positive integer, \(n\), is divided by \(d\) and the quotient and remainder are \(q\) and \(r\) respectively. In addition \(d, \;q\) and \(r\) are consecutive positive integer terms in a geometric sequence, but not necessarily in that order. For example, \(58\) divided by \(6\) has quotient \(9\) and remainder \(4\). It can also be seen that \(4, \;6,\;9\) are consecutive terms in a geometric ..

Consider the infinite polynomial series \({\rm A_G}(x) = x{\rm G_1} + x^2 {\rm G_2} + x^3 {\rm G_3} + \cdots \), where \({\rm G}_k\) is the \(k\)th term of the second order recurrence relation \({\rm G}_k = {\rm G}_{k-1} + {\rm G}_{k-2}\), \({\rm G_1}=1\), and \({\rm G}_2=4\); that is, \(1,\; 4,\; 5,\; 9,\; 14,\; 23, \; \cdots\). For this problem we shall be concerned with values of \(x\) for wh..