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sort of pascal's triange

Source: Spanish Mathematical Olympiad 1993 P2

August 1, 2018
number theoryPascal's TriangleSum

Problem Statement

In the arithmetic triangle below each number (apart from those in the first row) is the sum of the two numbers immediately above. 0 1 2 3 4 ... 1991 1992 19930 \, 1\, 2\, 3 \,4\, ... \,1991 \,1992\, 1993   1 3 5 7 ......    3983 3985\,\,1\, 3\, 5 \,7\, ......\,\,\,\,3983 \,3985    4 8 12 ..........   7968\,\,\,4 \,8 \,12\, .......... \,\,\,7968 ······································· Prove that the bottom number is a multiple of 19931993.
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