@MISC{_proposition, author = {}, title = {Proposition}, year = {} }

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Abstract

There are many relations known among the entries of Pascal's triangle. In [1], Hoggatt discusses the relation between the Fibonacci numbers and Pascal's triangle. He also gives several references to other related works. Here, we propose to show a relation between the triangle and the Fermat numbers f; = 2 2 ' + 1 for i = 0, 7, 2, •• •. Let c(n,j) be Pascal's triangle, where n represents the row index and / the column index, both indices starting at zero. Let aIn] be the sequence of numbers constructed from Pascal's triangle as follows: construct a new Pascal's triangle by taking the residue of c(nj') modulo base 2, then, consider each horizontal row of the new triangle as a whole number which is written in binary arithmetic. In symbols, let n (1) a[n] = Ys c*(n,j)2 J n = 0, 1,2,-,