MathDB
ASU 163 All Soviet Union MO 1972 numbers in a triangle table

Source:

July 3, 2019
combinatoricsalgebratriangle table

Problem Statement

The triangle table is constructed according to the rule: You put the natural number a>1a>1 in the upper row, and then you write under the number kk from the left side k2k^2, and from the right side -- (k+1)(k+1). For example, if a=2a = 2, you get the table on the picture. Prove that all the numbers on each particular line are different.
2 / \ / \ 4 3 / \ / \ 16 5 9 4 / \ / \ /\ / \