MathDB

2

Part of 1993 Spain Mathematical Olympiad

Problems(1)

sort of pascal's triange

Source: Spanish Mathematical Olympiad 1993 P2

8/1/2018
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.
number theoryPascal's TriangleSum