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arithmetic sequence a_n with a_1 prime factor >=i

Source: Mathcenter Contest / Oly - Thai Forum 2008 R3 p7 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 9, 2022

arithmetic sequencenumber theory

Problem Statement

Let

n,d

be natural numbers. Prove that there is an arithmetic sequence of positive integers.

a_1,a_2,...,a_n

with common difference of

d

and

a_i

with prime factor greater than or equal to

i

for all values

i=1,2,...,n

.
(nooonuii)