MathDB

Does there exist a row of Pascal’s Triangle containing four distinct values

a,b,c

and

d

such that

b = 2a

and

d = 2c

? Recall that Pascal’s triangle is the pattern of numbers that begins as follows https://cdn.artofproblemsolving.com/attachments/2/1/050e56f0f1f1b2a9c78481f03acd65de50c45b.png where the elements of each row are the sums of pairs of adjacent elements of the prior row. For example,

10 =4+6

. Also note that the last row displayed above contains the four elements

a = 5,b = 10,d = 10,c = 5

, satisfying

b = 2a

and

d = 2c

, but these four values are NOT distinct.

Problem Statement