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코딩 연습
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..
Let \((a, \;b, \;c)\) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such triangles together to form a square with length \(c\). For example, \((3, \;4, \;5)\) triangles can be placed together to form 1 \(5\) by \(5\) square with a \(1\) by \(1\) hole in the middle and it can be seen that the \(5\) by \(5\) square can be tiled with tw..