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Solution of problem T10/363 in M&Y

September 24, 2007 in Mathematics and Youth Magazine | Tags: | 3 comments

\left(a-\dfrac{1}{b}\right)\left(b-\dfrac{1}{c}\right)\left(c-\dfrac{1}{a}\right)\geq \left(a-\dfrac{1}{a}\right)\left(b-\dfrac{1}{b}\right)\left(c-\dfrac{1}{c}\right)\\ \forall a,b,c\in [1,+\infty).

Solution of a my student.

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Solution of problem T6/363 in M&Y

September 22, 2007 in Mathematics and Youth Magazine | Tags: | Leave a comment

Find all (x,y)\in\mathbb{Z}^2 such that x^{2007}=y^{2007}-y^{1338}-y^{669}+2.

My solution.

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Problems in Mathematics and Youth Magazine, 2007 , Issue 9

September 22, 2007 in Mathematics and Youth Magazine | Leave a comment

For Lower Secondary Schools

1. The first 100 positive integer numbers are written consecutively in a certain order. Call the resulting number A. Is A a multiple of 2007?

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Solution of problem T12/363 in M&Y

September 22, 2007 in Mathematics and Youth Magazine | Tags: | 1 comment

Let f:\mathbb{N}\to\mathbb{R} be a function such that f(1)=\dfrac{2007}{6} and \dfrac{f(1)}{1}+\dfrac{f(2)}{2}+\cdots+\dfrac{f(n)}{n}=\dfrac{n+1}{2}\cdot f(n)\forall n\in\mathbb{N}. Find the limit \lim_{n\to\infty} (2008+n)f(n).

My solution.

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Solution of problem T7/363 in M&Y

September 21, 2007 in Mathematics and Youth Magazine | Tags: | Leave a comment

Let (x_n) be a sequence given by x_1=5,x_{n+1}=x_n^2-2(n\geq 1). Calculate \lim_{n\to\infty}\dfrac{x_{n+1}}{x_1x_2\cdots x_n}.

My solution.

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